Approaching Infinity

Intervention Time Resources Needed

2012-01-12T20:26:00.000-06:00

My school is going to be starting a scheduled intervention time for students soon. Our entire middle school has been split up into four academic groups based on MAP scores and classroom success. Since I will be taking the students that need extra help in math, I am still kicking the tires on how I want to approach this situation.

I am probably going to have around 30 kids between myself and a teacher's aide for the intervention time, but the students are a mixture of 6th grade math, 7th grade math, pre-algebra, and Algebra 1 students. Since I do standards-based grading, I will be having the students work on the learning targets they have struggled with during the school year. Some reteaching will be necessary, but for the most part, these students will be just doing some skill-based practice. This is where I am hitting a few snags.

There's no way that I will be able to individualize the problems that each student needs to work on every day without using technology. I also think that this will be the quickest way for the students to receive feedback on the problems. I have a short list of some resources that might help me in this situation, but I'm wondering if anyone else has a better suggestion. Here are a few of the resources that I have looked at with a few pros and cons listed:

Khan Academy: I don't think there is a large enough database of skills to meet the concepts that all my students need to work on. Most of the skills seem to fall in the K-5 range, so it's not much of a help.

TenMarks: I like this site as it is pretty customizable and has a large selection of questions (many of which even focus on problem solving). The good thing is that it's free, but several times during the year when I have wanted to use it, the website is down. I cannot use this resource if it is not reliable.

IXL: This would also be a good resource to use, but it's expensive. I might try the 30-day trial and see if my principal could spring for a subscription, but I'm not sure that will be possible.

ALEKS: I supervised a high school make up course last summer with students who used this program. It was pretty detailed and doesn't have multiple choice answers (which is an anomaly), but since it is a program, it doesn't allow the students to have a free-range choice of all the concepts. It also costs money.

Manga High Math: Although it is mainly a math games website, it does have skill-based questions. I've had a couple students use it this year, but the questions are pretty bad and I probably shouldn't even consider it.

Those are all the resources I have experience with. Does anyone have any insights to another website similar to these that might meet my needs or any other suggestions based on the ones I have listed?

Math Teacher Interview Questions

2011-08-02T22:29:00.001-05:00

Preparing for a job interview is not only important for the person being interviewed, but also for the interviewers. Asking all the right questions can get you a good idea of who the candidate is and how they operate as a teacher. Here is a list of good interview questions that Lisa and I gathered from the responses we received via Twitter.

What would your dream school look like?
Share with me what you think a good piece of mathematics is - something you really like.
How would you make math class great for the students who feel like the "dumb kid?"
Do you have any experience with Web 2.0 tools?
Are you familiar with the Common Core State Standards for Mathematics? NCTM's Principles and Standards for School Mathematics?
Why did you choose to become a math teacher?
What is your relationship with mathematics? Why do you love it and why should anyone care about it?
How do you make the content relevant and engaging for all learners? How do you make the content more accessible?
Tell me about a lesson that went well and why.
Tell me about a lesson that didn't go well and why. How might you improve that lesson?
How do you use technology in the classroom? As a personal/professional learner?
What skills and technologies are you most interested in improving upon or learning?
Do you find any particular courses/subjects/topics intimidating?
What professional materials (books, websites, blogs) do you read?
Describe a typical day in your classroom.
Which math is your favorite to teach and why?
How do you teach coverage of all topics while teaching students how to think/problem solve?
How would you work with a particularly difficult parent or student?
How do you incorporate problems that promote reasoning and sense making into your classroom?
How do you feel about implementing backwards design into your curriculum?
How do you determine a student's grade?
What is your homework philosophy?
What do you do when a student doesn't understand a concept?
How do you differentiate instruction in a class with students who can't multiply and students who understand complex math ideas?
What were your favorite classes in high school and/or college?
How do you determine what you teach?
How do you get students to practice math?
Give an example of a lesson when your students were really engaged.
How do you get students interested in the problem solving process?

It was also suggested to have the candidate substitute for a class, teach a lesson, and follow that up with some reflection with the interviewers (similar to a formal observation).

Hopefully some of you (interviewers and interviewees) will find this list useful in the future. Add any others that you can think of in the comments!

Reaction Time Test

2011-07-05T22:01:00.000-05:00

I wanted to review mean, median, mode, and range with my students by having them use data that was meaningful to them. I saw this reaction time test and thought this would be fun way to review these skills. I also wanted the students to recognize how outliers affect the mean. I had them use this handout while working to keep track of the data.

The lesson went well, but a funny thing happened while the students were collecting their data. We've all had those unintentional things happen in a lesson that have turned out to a blessing in disguise and this was one of them. One student was collecting their data and forgot to record one reaction time. The website shows the mean reaction time after each click, so she had this information:

What was the time for the 5th attempt? Behold a new, more challenging problem! I love it when these things happen.

WCYDWT: Basketball Update

2011-07-05T20:06:00.000-05:00

A while back, I posted about an online basketball game that I felt could be used in a quadratics lesson. I finally had a chance to try it out this year. Here's what I came up with.

The day before this lesson, my students did some exploring with quadratic equations and their graphs by using this Geogebra applet. The next day, I put the Multiplayer Basketball game on the SMART Board and took a couple shots so they could get the idea of the game. Then I put the following pics on the screen and asked them to record whether or not the shot was going to go through the hoop.

I asked the students how they could figure out the actual answers (besides playing a video). A few noticed that the path of the ball formed a parabola and that the location of the mouse on the screen seemed to be the vertex of the graph. They also said that the if the portion of the shot that is already shown could be reflected across the axis of symmetry (I paraphrased that), they could figure out if the shot went in.

Alas, they busted out these Geogebra applets to find some answers (Shot 1, Shot 2, Shot 3, Shot 4). After they found a graph to fit the shot, I tried to make it a little interesting by having them place wagers on their confidence of each guess. I gave each of them 50 points to divvy out between the four shots. They had to wager at least 5 points on each shot and they had to wager all 50 points. If they guessed correctly, they got to double their points. I had a competitive class, but they didn't seem to buy into this. The purpose of this was to get them to pay attention to accuracy. Some of the shots hit the rim, but a few of my students found the graph that was "close enough" to the path of the shot causing them to guess incorrectly.

Overall I thought they lesson went very well. They were very engaged in the lesson and many of them made comments about how they enjoyed this lesson on my end-of-year evaluations. One thing that didn't go so well (besides the wagering) was the timing of this lesson. My students worked on the applets on a Friday, so they didn't get to see the answers until Monday. I think that took out a lot of the suspense of the shots that were hard to guess the answer to.

If you would like to try this out on your own, click here to download all the goods. The file includes all the pics, Geogebra files, the handout, and the answers. If you have any suggestions for improvement or if you try it out and make improvements, please share!

School Year Recap

2011-07-01T13:32:00.000-05:00

I've been wanting to write a year-in-review post for a while, but between summer school and grad class assignments I haven't found much time or motivation. Here's some of the highlights and lowlights of the 2010-2011 year:

I have had increasing frustration with using Saxon Math textbooks in my class and we don't exactly have a curriculum without the textbook. As a result, I put together a list of benchmarks and ditched the textbook for the entire year in my 8th grade class. It was a lot of work (especially with no one to collaborate with), but it was totally worth it. The 6th grade book is the next one on the agenda.

Since I had new benchmarks from which to work from in my 8th grade class, I thought this would be the perfect time to dabble in SBG. Again, I'm very happy that I made this decision. I made sure to do lots of explaining of grading philosophies at the beginning of the year to make sure they understood why I changed (I had my 8th graders for 3 years). I also had my students do several reflections in the first quarter just to make sure they understood how everything was going and what their thoughts were. All the students loved it as it gave them a better focus for what to learn and they knew exactly what they needed to improve upon. I even made one of those fancy data walls, similar to this. My administrator loved it and it was useful to me to drive instruction, but I'm not sure my students found it as useful as I would have liked.

One thing I was worried about with SBG was my students' responsibility in doing reassessments. I was completely wrong on this. I did have a high/over achieving class, but every single one of them signed up for at least one reassessment during the year. I don't have the numbers in front of me, but I'm willing to bet that at least 80% of them signed up for more than 5 reassessments. Good for them!

This leads me to a problem I had with my SBG system. Too many reassessments! I had students fill out a slip of paper to sign up for reassessments and they needed to give me at least 24 hours notice. I also kept a document of all the reassessment problems. However, I spent way too much time creating the reassessments. Even with my organization, I had to write (or copy/paste) at least one reassessment every night and there were a couple occasions where I had 15 to write. A couple is fine, but doing all of these takes up a huge chunk of time and I don't always have that to spare. I'm thinking about putting reassessment problems on the regular assessments this year to avoid the constant flow of paper work. Any other suggestions?

Because I dropped the textbook, my class structure was way more loose. I made sure to take more time with concepts so the students understood everything. I wasn't worried about doing certain activities because "they took too much time." I did a lot more inquiry and problem solving. The best lesson I got out of doing this was when I did the Holes lesson from Dan Meyer. I didn't give them any direction other than the question, "Are you curious about anything in this video?" I had kids that normally struggle ask all the right questions and give excellent reasoning. It was amazing.

I did some "flipping the classroom" for about 2 weeks with my algebra students with mixed results. Some liked it, some hated it, and some were indifferent. My feelings are that it was a terrible idea. I think most of the students just watched the videos rather than trying to actively learn from them. I also think I picked a bad part of the year to try this out. The graphing linear equations unit is always the toughest part of the year for my students and the frustrations with learning this along with this new method of learning did not pair well.

I was put into this situation for about six weeks. I was very positive about it and was willing to make it work, but it was very stressful for me. Thankfully the idea was rejected and I will have a "normal" job this coming year...

...in a new building. Due to some budget cuts and other opportunities, I chose to switch buildings in my district for the upcoming school year. I'm disappointed that I won't get to continue working closely with my students and colleagues in my old building anymore, but I couldn't pass at the chance. Nervous and exciting times lie ahead.

WMC Day 2

2011-05-06T22:27:00.000-05:00

Four more sessions were on the schedule today and I saw some pretty amazing things done by classroom teachers.

The early-riser session was on improving students' understanding of math vocabulary by having the students participate in "Motion Monday." This teacher focused on 28 vocabulary words throughout the school year. For every word, she had the students get out of their seat and do a motion that represents that word. Some were pretty simple (make an obtuse angle with your arms) and some were a little more complicated (the factors motion was a combination of listing all the factors of 24, clapping their hands, and snapping their fingers). The students did these motions every Monday along with giving their own definition of the word.

The thing that really struck home with everyone was the data she provided on the effectiveness of this program. She gave her students a pre-test on theses words during the second week of school and then again at the end of the school year. Last year's 6th grade class averaged a 68% in September and increased their score to 92% in April. Even better, when she tested those same students at the beginning of this school year they averaged 94% correct. A 2% increase over the summer! Parents even commented that their children practice these motions at home, so maybe that helped with the retention of the words over the summer. I'm definitely sold on this idea. I've done motions like these in the past, but not to the extent that she's done. I'll be giving this a shot next year.

My second session was on using the art of storytelling to enhance math instruction. This was definitely a different approach to the story telling aspect that Dan presented yesterday. This teacher liked to have his students work on difficult math problems (think: those homework problems at the end of each lesson in the textbook), but he noticed that the students' interest in these problems would wane as the year went on because they were not motivated to work through the difficulty of these problems. To increase the motivation, he wrote books that included these problems within the story. Here is a link to his website where you can view a sample of a story. I'm not sure where he found the time to do this, but it was very creative. Make sure you check out the posters that he created too.

The third session was on the importance of using real-world data to help students learn to not only find measures of central tendency, but to also help them learn to question and analyze data. I don't think the ideas here were anything groundbreaking, but the presenter provided us quite a bit of data that we could use in the classroom. I'm not sure how long it took him to collect all that data, but I'm glad he shared!

There wasn't much to choose from for the last session, so I attended a session on teaching fractions. I didn't really pick up anything new, but it's always fn to talk about the different representations of fractions and how to properly teach them. Fractions can be such a problem area for students, so it is interesting to hear that the CCSS is having students focus on the understanding of fractions for much of their 3rd grade year. Any thoughts on this?

WMC Day 1

2011-05-05T20:47:00.001-05:00

I attended five sessions at the Wisconsin Math Council Conference today. Here are a few of things worth sharing.

Dance Dance Geometry

This came from a session on inviting play into your math classroom that turned into a college lecture on some Piaget stuff. They did share the idea in this video but didn't have any links to the animated file. Anyone know where I can find it? Google didn't help me.

I went to two of Dan Meyer's sessions. I was familiar with most of what he talked about from reading his blog, but it's nice to hear it all put together rather than reading it in segmented blog posts. Both of his sessions were packed I didn't hear one negative comment, which is quite unusual from a group of teachers. Here is a link that he gave us with all of material that was in his talk. Kudos to the WMC for booking Dan and inspiring all those teachers that haven't had the chance to read his blog.

The final session I attended was by Ed Zaccaro on Five Real-World Math Investigations that Will Teachers and Students. It was pretty good, but I saw Ed speak when I was in college and I'm pretty sure that most of this material was in that same presentation (although it was packaged under a different name). He did another presentation earlier in the day. Here is his website where you can view all the slides from all his presentations.

I did attend a session on implementing RtI in the secondary math classroom, but the presenter ran out of time. I primarily attended this session to see different ways to provide intervention time into a structured schedule day, but I didn't get to hear those.

WCYDWT: Parking Lots

2011-04-04T18:40:00.000-05:00

I'm convinced something pretty good can be made out of this problem.

When I first looked at this problem, I wondered if the dimensions of the parking lot were even reasonable. I was surprised to find that 9 by 18.5 actually is a reliable size for a parking stall (Source: Page 5). I played around with the numbers in the angle parking lot and those look to be accurate too, although I'm not quite sure how they got 17.5 feet for the height (I keep getting 19.4).

So what would you do with this problem? I didn't even look at the questions and I immediately began to wonder why someone would choose perpendicular parking over angle parking and vice versa. I think students would enjoy working with this provided they are given the right hook. Maybe they could be in charge of choosing the best setup for a parking lot. What do you think?

A Penny for Your Thoughts

2011-03-12T15:50:00.000-06:00

Here's a little hypothetical situation for you. Let's say that you are part of a district that has two middle schools. Neither school is very large -- one has around 95 students and the other 120. You teach in the smaller building and the teacher in the larger building has recently retired.

Since you have been successful in your time at your school, you have been approached to teach math to the entire district's middle school students. Since the schools are 15 minutes apart, you will have to teach in each building on alternate days. The students will not be on a block schedule, but while you are at one school, the other will be learning via some type of online learning. It is uncertain how that will work right now; it may be with a VoIP service or maybe even with video lessons that students would watch independently. The students that are not in your building at the time will not be without any adult help as a teacher's aide with good math and discipline skills will be available.

I was approached with this scenario recently. I'm not necessarily for or against this idea yet, but I certainly have a large list of concerns. What are your thoughts? Do you know of any schools that do something like this?

Gratuitous Plug: Alternative to Whiteboards

2010-12-28T19:33:00.000-06:00

I don't know how I missed Frank's post on "The $2 Interactive Whiteboard" when it was originally written, but I caught later when it was awarded the 2010 Most Influential Blog Post. After reading it, I want to toss out a tool that is similar to whiteboards, but one that I prefer to use.

A few years back, I bought a class set of whiteboards that have a coordinate plane on one side. I liked them, but I didn't use them a lot because I felt they were limited in their use (size and lack of versatility). Last year, I had several days of professional development where I was able to observe another teacher using these folders where you can slide a piece of paper inside and write on the folder with a dry erase marker - similar to a restaurant menu. They worked exactly the same as a whiteboard, but you could place any kind of a template inside the folder to get maximum use out of them.

I ended up buying a model similar to the one from Nasco, but from EAI. The SmartPAL folders are much easier for students to use as they are side-loading rather than top-loading. When I observed the teacher using the Nasco folders, the students had a really difficult time sliding their templates inside the folders. My students have no problems placing the templates in the SmartPALs.

I also bought the Big Book of Middle School Communicator Classroom Templates. It is a great resource of ideas and templates to use with the folders. Not all of the ideas are great, but the templates are a time saver and you can at least take some of the ideas and tailor them to your needs.

The SmartPALs have all the advantages of Frank's whiteboards (except for the size), but they provide a little more versatility in that you can place any template inside the folders (number line, coordinate plane, hundreds grid, function machines, unit conversion connectors, etc.). The different colored folders can also allow for differentiation. The SmartPALs may be more than $2, but their value to me is more treasured than my set of whiteboards.

The Mathematical Genius

2010-12-28T09:59:00.001-06:00

I never watch 20/20, but I somehow caught the show the night this story was on. I showed it to my 8th graders the day before the holiday break. Before I showed the video, I asked them to draw at least three representations of the number nine on a piece of paper. I had all sorts of representations: 9, nine, 8+1, a square with an area of nine, 3 squared, nine dots, IX, etc. Then I gave a little intro to the video and told them to pay attention to how this man represents his numbers. It's pretty amazing how his brain works.

Edit: If you are viewing this on Google Reader, you will probably have to click through to view the video.

Organizing Those Stolen...err Borrowed...Lessons

2010-08-06T12:42:00.000-05:00

Amber at Maximizing Learning wrote a post a little while ago about how she has found so many great lessons via blogs but has a hard time keeping them organized. I commented on the same problem, but not everyone reads comments so I will share what I did here.

Over the last year or so, I have saved many great lessons, games, and activities that I wanted to use. Most of the time, I completely forgot about the lesson that I saved when it came time to teach that topic. This summer I spent time sifting through my saved bookmarks on Delicious and my starred blog posts on Google Reader and put them in one location. Since I teach four different classes, I created a spreadsheet with a sheet for each class. I listed the concept each lesson falls under and the grade I am planning on using the lesson with. Now when I am planning a lesson, I will always look at this spreadsheet first. Hopefully this can be beneficial to others as well. If you have any other lessons that I should add, let me know.

Lesson Ideas Spreadsheet (6th, 7th, 8th, Algebra)

My Standards-Based Grading Plan

2010-08-05T12:47:00.000-05:00

Along with a lot of my fellow math edubloggers, I am planning on giving Standards-Based Grading (SBG) a shot next year. I've read lots of blog posts and had some conversations on Twitter to help me through the process of setting up a plan of action. I'm definitely just copying the ideas of others until I can get into the flow of the school year. I have no idea if I will have to make changes to my plan (I probably will), but I'm not the type to obsess over minute details. If I have to change something in October, I'll do it and the students and myself will adjust.

Now for my plan: Go read this. I won't rewrite everything that I'm doing because Dan already did.

My students will be keeping track of their scores using the method discussed here. My students keep a separate "grade folder" in my room, so the tracking list will remain in the folder throughout the year. Whenever I hand back an assessment, they will update the list. As for reassessments, my plan is to have the students come in for reteaching one day and a reassessment the next. They will not be able to do both on the same day. Knowing my students, I'm a little skeptical of this idea because they will not want to use two days to reassess on one topic. I have a feeling I will have to do a lot of preaching about being responsible this year.

Like I said before, I'm sure I will have to make adjustments along the way and I will reflect on those changes. Stay tuned!

SMART Board Training

2010-08-05T12:12:00.001-05:00

Last spring I conducted an inservice session about the SMART Board. I was planning to share some of the lesser known features that some teachers might not use, but the people that attended wanted to know things like, "How do you turn it on?" or "Can I use the SMART Board pens to draw on my computer monitor?" I'm sure some people were frustrated because they wanted to learn new things and instead they got a review of things that can be figured out in 5 minutes of playing around.

I made a file to demonstrate some of the interactive features that are in the Gallery, the transparent screen, the print screen, and useful links. If you are looking for new ideas or if you have to present SMART Board ideas at a meeting, use and modify my file and save yourself some time. Obviously the file was tailored to fit my needs, so if you have any questions about what I meant on the slides, post them in the comments. If you see and tiny paperclips or globes on the slides, you can click on them to open a file or a link.

Click here to download the file.

Math Formulas Bookmark

2010-08-05T11:54:00.000-05:00

I made a bookmark that contains several formulas and conversions for my students to use in their textbooks. Many textbooks have this information on the inside cover or on a few of the resource pages in the back of the book, but mine do not. I took screen shots of some files that were on the classzone.com website and made them fit onto a standard sheet of paper. I'm going to print these back to back on card stock.

Click here to download the bookmark. (Note: The bookmarks will look severely off-center on Google Docs, but if you download the file and view it in Word, it will look better.)

WCYDWT: Basketball

2010-06-23T17:48:00.001-05:00

This is probably just a ripoff of Dan's similar post, but I think students will have more fun with this using the same idea. Go check out this Multiplayer Basketball game. Have fun, I'll see you back in 5 minutes.

There is a lot of math that can be discussed with this game. I first saw this game from somebody on Twitter a while ago (I don't remember who to credit). They mentioned this game as being a WCYDWT for the histogram shown after each shot. I think the graph would be slightly useless to most students as they would be focused on making each shot, so by analyzing the graphs to understand them might actually make them useful to the students.

What information do we need to interpret the graph? Which graph would be the best to use? What are the interval ranges? What are the possible scores that a person could have achieved on one shot to move up an interval? There are probably more that could be asked, so post some in the comments if you have any.

What's pretty sweet about this game is that you can set up a private game for your students to play against each other. The results don't have to be recorded in real-time either, so you could have one student play while another records results, then flip-flop.

Since I am more interested in the game play, I thought about Dan's post. Have the kids play a few games to get an understanding of how the game works. Record video of a game and take a screenshot of one of the shots.

If I click the mouse, will I make a basket? The students could insert the image in Geogebra and play around with quadratic functions to find out. Then play the video for results. What did I miss?

Hands-On Difference of Squares

2010-06-20T20:20:00.000-05:00

This activity is similar to the hands-on paper activity I posted the other day with binomial squares. This one will help students visualize the difference of squares.

Start by getting a square piece of paper, just like in the other activity. I highlighted the fold crease so it is more visible. Have the students place a black dot again so that when you make the folds in the next step, it is more visible.

Make vertical and horizontal folds through the black dot. This time, cut out and remove the square in the picture.

Time to do some labeling. Students should write these right on the paper.

Find the area by subtracting the area of the missing square.

So where does the difference of the binomials come into play? This is where the students will really have to do some thinking. Cut the paper in halves on the diagonal crease from the first picture and place them together to form a rectangle.

Have the students figure out the dimensions of the rectangle and label them on the paper. To find the area of this rectangle, you have to multiply (a + b) and (a - b). What is the product of the binomials? Has the area changed? Light bulbs will turn on.

I got both of these activities from a math conference this year. I really liked them and really wanted to use them this year because my students would make simple mistakes on these two concepts because they didn't think; they just wanted to do the "short cuts," albeit incorrectly. I thought this would help cure the sickness...and then I forgot to do them. There's always next year.

Has anyone else done this in your algebra class? How did you do it differently?

Hands-On Binomial Squares

2010-06-17T17:40:00.000-05:00

How many of your algebra students do this?

How do we get them to stop doing that? You could show them a visualization similar to this and hope they remember it, but chances are they won't.

Why not have the students create this visualization? You can give them a few directions (Label this a, label that b). They can figure out the rest.

Start by getting a square piece of paper. I did this trick to make the paper square. You will have a diagonal fold crease. It was hard to see on the picture, so I highlighted it.

As you can see in the picture, I made a large dot with a sharpie. This is to help the students see where to make the vertical and horizontal folds seen in the next picture.

Do some labeling. The students can label the dimensions on the paper.

Find the areas. Again, the students can write these on the paper.

Combine terms and you're done!

An alternate to this would be to use numbers instead of variables first, then switch to variables on the flip side. I will post another activity similar to this with the difference of squares when I get some time.

Factoring is Fun!

2010-05-01T20:14:00.000-05:00

This is the comment that I got from several of my students this year. Our high school uses CPM for struggling algebra students, and one of the teachers showed me the "Diamond Problem" method for factoring. She mentioned that the kids loved them and recommended that I try them. Now I am recommending that you use them as well. Here are a few resources to use to learn how to use Diamond Problems if you are unfamiliar with them:

Diamond and Box Factoring PowerPoint file

David's video explanation:

Teach Lazy

2010-04-11T19:43:00.000-05:00

The book that I have been reading for my online grad class is an extended handout of the book Windows on the Future by Ian Jukes and Ted McCain. Here is a quote from the book that I particularly liked.

"My job as a teacher is no longer just to stand up in front of my students and show them how smart I am. My job is to help them understand how smart they can. My job is to teach lazy. My job is to shift the burden of responsibility for learning from me to them, where it belongs."

Word Problem Help

2010-03-15T19:50:00.000-05:00

I've been running into some problems with my algebra students lately. We have been solving systems of linear equations and inequalities and they have been doing just fine with solving these when they are given the equations/inequalities.

There are a few word problems thrown into each lesson to give them a real-world scenario where they would possibly use systems. I like these problems, but my students are having a hard time setting up the equations/inequalities.

How important is it for my students to understand how to do these problems? To me, my objective for these two lessons is for them to correctly find the solution(s) to the systems. If I have students that are able to solve the word problems that go along with it, I take it as a bonus. When I was in high school, I always remember having a tough time setting up the equations for word problems too, so I think that is why I don't place a lot of emphasis on these problems. However, I feel that I may be passing on important concepts for my students to understand. Any advice?

I Tell Lame Jokes

2010-03-10T20:08:00.000-06:00

I recently had my 8th graders conduct surveys to collect qualitative and quantitative data. I used this opportunity to integrate several pieces of technology, including the advanced uploading of files feature in Moodle (which works great), Google forms, and graphing with Excel.

A few groups decided to survey their peers to find out if they thought I was funny or not. The choices were: Yes, No, and Definitely Not. I guess they didn't understand bias questioning, although they did reflect in their responses that "Definitely Not" should have been omitted. The same group also reported that most students agreed they have heard me tell around 30 lame jokes. That's funny because I thought my students could count higher than 30.

Time to Weigh the Hippos

2010-03-06T08:49:00.000-06:00

Here is an interesting, yet challenging question that involves systems of linear equations.

Zookeeper Robin has just received four pygmy hippopotamuses as an anonymous donation to the Wild Zoo. As usual, she wants to weigh the new arrivals and record all vital statistics. Unfortunately, each hippo alone is too heavy to be weighed on her small-animal scale and her large-animal scale begins reading at 300 kg – more than any of the hippos weighs alone. Her solution? Weigh all possible pairs. She does this and records the following pair weights: 312 kg, 444 kg, 356 kg, 378 kg, and 466 kg. Then she tries to weigh the final (and heaviest) pair and the scale breaks! Use the above information to find the weight of the heaviest pair and the weights of the individual hippos.

Multiplying and Dividing by Powers of 10

2010-02-28T21:01:00.000-06:00

I found a mnemonic device from a website a while back that helps students remember the rules for multiplying or dividing by powers of 10. They start out by writing the letters d, i, and m.

The "d" stands for divide, the "m" stands for multiply, and the "i" is merely there for the dot which represents the decimal point.

Let's say we want to multiply by a power of 10. Draw an arrow starting from the point to the "m."

Since the arrow is pointing to the right, we need to move the decimal point to the right. The same thing works for dividing. Draw an arrow starting from the point to the "d."

Since the arrow is pointing to the left, the decimal point needs to be moved to the left when dividing.

Coordinate Plane Drawings

2010-02-10T19:50:00.000-06:00

Last fall I saw a few blog posts on creating coordinate plane drawings using Geogebra, Excel, and DigitiseImage. While the logos that these gentlemen created are great, my students wouldn't exactly be excited to create logos of teams they have never heard of.

I used Jeff's directions to create logos of the Green Bay Packers, Milwaukee Brewers, and Wisconsin Badgers. Even if your students don't like these teams, I recommend using those blog posts as guidelines for creating your own. I also created a large-scale coordinate plane to use with these drawings.

Differentiate Math Homework

2010-02-07T10:44:00.002-06:00

If you want to differentiate your math homework, here's a good way to make it work.

Start by creating your normal set of problems. For this example, we'll create 15 problems. The problems should be of increasing difficulty. Problems 1-10 will be called set A and problems 6-15 will be called set B. Students can choose whether to do set A or B on their own. If you don't think students will be motivated enough to choose set B on their own, you can either assign students to the two different groups or offer a bonus point for students who choose to try set B.

Anybody have any other methods for differentiation?

Update: I received a comment about this post on Twitter via @vtdeacon:

"How about instead of choice actually giving out two or three different homework sheets with problems set at each students level?"

I think this is a perfectly good way to do differentiation, but I think most teachers would scoff at doing this because it means extra work. It means making two or three separate sheets per concept, making copies of each of these sheets, and keeping track of how many copies to make for each group of students. If I had to do this for 6 classes a day, I wouldn't do it for long. The way I presented only needs one sheet and the students can keep track of the groups they are in.

New Teacher Advice

2010-01-17T14:54:00.001-06:00

Back in the fall of 2006 when the NCTM Regional Conference was in Chicago, my college professors gave my peers and me the chance to attend for a fraction of the normal cost. It was a great experience and I acquired some useful information. One session was a speaker giving advice to new and preservice teachers. I found the file from the speaker recently and thought I would share it. I remember looking at these slides quite often during my first year.

Here is the link to the file.

Weekend Shopping Gem

2010-01-04T20:35:00.001-06:00

I picked up a few of these while shopping the other day. Should be useful during the percent of change lesson.

Here's the good info.

Note to Self

2010-01-04T20:09:00.001-06:00

This is my best Norm MacDonald impersonation.

Note to self: Next year, do not plan on teaching any concepts on the first day back after a long break. You did this today and flopped. The kids were still sleeping the first three periods—so were you—and the other classes did not want to be at school yet—neither did you. To top it off, the students seemed to forget everything that was learned the two weeks prior to the break. Instead, do some sort of active learning/review game. Maybe even do one of those trash can basketball games that everyone is talking about.

School Year Resolutions Checkup

2009-12-31T11:19:00.000-06:00

It's that wonderful time of the year when everyone makes resolutions they will never keep. That reminded me I made some resolutions back in late August for the new school year. Plus, it's almost the end of the first semester so I think I should see how I'm doing.

1. My first goal was to reward students for doing a "good job" more often. I think I have done a pretty good job of this. I've created an award called the Spartan Circle and I choose one student from each grade level every other week. I use the same criteria as this picture shows. I give them a pretty cool looking certificate with my signature on it - which is the best part of the award in my opinion. The also receive a coupon for a free pass on a test/quiz question. On top of that, I take their picture and put it on my Spartan Circle bulletin board for the whole class to see. I think I could do a better job of promoting the Spartan Circle because it might be losing some of its luster, but many of the students are definitely proud and excited to be picked.

2. The second goal was to make math more real-world applicable. I have done much more in this area than I did last year, but I still have a lot of work to do. I spent some of my break reading through Dan Meyer's blog. Now that is relating math to the real-world. I still feel that in many ways I did this better in my first year as a teacher. Back then, I didn't have a textbook to work with and I also had a math teacher mentor who guided me with unit plan outlines. At my current school, the thought is to use the textbook as the curriculum rather than a resource. To top it off, the textbook is Saxon. I am slowing developing materials that stray from the kill-and-drill ideas of the textbook, but it's going to take some time. I have to keep reminding myself that Dan stayed up until midnight on many days to create that stuff. I need my precious sleep.

Enough ranting. What have I done to meet this goal? The 8th graders have done a cost of living project again - which reminds me that I still need to share that idea. After the classes are done with quizzes or tests, sometimes I show videos from The Futures Channel. We have some good discussions. I also created the Careers in Math project. All of these are general ideas though. I'll keep working on it.

3. The third goal was to keep my composure through my busy schedule. I made it through the fall, which was going to be the toughest part. I juggled the beginning of the school year craziness with completing my first year as the 7th grade football coach. Piece of cake.

I'm still on the school's Leadership Team. Not too much extra work other than planning for subs every once in a while. However, we are planning a Math Night to get the community more involved in our school. Since I'm the only math teacher in the middle school, guess who's planning all the activities? That might be a little tough.

Being the Staff Tech Support person isn't a lot of work, especially when you like doing that stuff. In fact, I like it so much that I will be starting my Master's Program in Educational Technology. This will be another test for me to meet this goal, but I have no doubt I'll pass.

I hope some other people that made these resolutions take some time to reflect on how they've done. Even if you haven't kept your resolution, it would be good to reflect on why you haven't been able to meet your goal. Maybe you can even make a New Year, School Year Resolution.

Converting Units of Measurement Using Connectors

2009-12-29T16:01:00.004-06:00

I'm sure most math and science teachers at the secondary level cover dimensional analysis at some point, so this lesson might be very useful to you. In the past, I taught it by moving left to right like in this example. I've even used NLVM's interactive converter to help my students out. They worked ok, but I still had students slightly confused and they made small errors that caused them to get wrong answers.

This method is called Connectors and it can be compared to playing Dominoes.

Directions:
1. The students all start with this handout. I will use the example of converting 90 mi/hr to ft/sec.
2. Begin by writing the starting rate in the bold, center "domino." In the upper right diamond, write the target rate.

3. Take another piece of paper and cover up either the top or the bottom of the original rate. This helps students focus on one specific unit. I will cover the bottom first.
4. Find an equivalent measurement that helps reach the target rate. Notice that the "mile" units align with each other, just like matching numbers align in Dominoes.

5. Since we have our units in feet, we can slide the extra piece of paper to cover the top portion of the original rate. Just like in step 4, we want to find an equivalent measurement that helps us reach the target rate. In this case, your students might not know the conversion from hours to seconds, so I will do it in two steps.

6. Slide the extra piece of paper down one row to focus on the "minutes." Find an equivalent measurement.

7. Take off the extra sheet of paper and you will be left with a good visualization of the 4 fractions needed to multiply.

8. Write the fractions, cancel the units, and multiply and divide like normal. There's your answer.

Ideally, your students might only use the paper template a few times and then they'll get the hang of it. The key thing that is different is starting with the original rate in the middle and working outward.

One thing to do that might be a little more hands-on is to use note cards instead of the template. This way the note cards can slide to be aligned to make the fractions even easier to notice.

Snake Game

2009-12-28T19:30:00.000-06:00

A while back, I created a popular dice game called Snake (others call it Skunk) using Scratch. Scratch is a type of programming language created for young people or novice programmers. If you search through their galleries, you will be able to find lots of other math related activities.

Original link to this project

Killer Number

2009-12-28T19:13:00.002-06:00

Objective: To be the person with the most points at the end of 5 rounds.

Materials: Every person needs to have a handout of the table below. Another option is to project the table and have the students make one in their notebook. The teacher needs a number cube or die; I use the one in SMART Notebook so all the students can see.

Rules:
1. Roll the die twice. These are the round points. Have the students record these two numbers in each row in the "Round Points" column in their table.
2. Roll the die again. The result is the Killer Number. Record this number on the board or somewhere easily visible to the students. If at any time during the game the Killer Number is rolled and a student is standing, their round total is automatically 0.
3. There are 5 rounds for the students to participate in. To start each round, students may begin by standing. However, if a student feels that the Killer Number will be the first number rolled, they may start seated and their round total is the sum of the round points. The round points are always guaranteed points (unless a student is standing when the killer number is rolled).
4. Roll the die. The students who are standing record the number in the "Running Total" column. At this time, students may choose to be seated. Once a student sits down, they may not re-enter the round. They must add the sum of the round points and the running total and record the result in the round points.
5. Continue to repeat step 4 until all students are seated or until the Killer Number is rolled.
6. Once a round has been completed, all students should have their round total completed and be ready to start the next round. All rounds have the same rules.
7. At the end of the 5 rounds, students should add the round totals up to find their total points. The student with the most points wins

Here is a link to the Killer Number table in Google Docs. Enjoy!

Smart Cards

2009-12-20T21:30:00.001-06:00

This isn't a new idea by any means, but I took the idea and created a template for others to use. I originally took the idea from a Marilyn Burns book, but I've seen the idea on other websites.

Rules: Have a student pick a number from 1 to 31. Show them each individual card. Ask the student if their number appears on the card. After they have replied to each card, watch them become amazed as you tell them their number. Here is the template I made.

If you aren't sure how this works, all you need to do is keep track of the students responses and do some quick adding. If the students number appears on the card, add the number in the upper left each time. For example, if the student's number was 9, they would say "Yes. No. No. Yes. No." You would have to add 1 and 8 because those are the numbers in the upper left that correspond with the students responses.

I printed these cards on card stock, laminated them, and attached them with a ring. I have done this activity numerous times and my students still cannot figure out the trick, yet they keep asking me to play it because they think they can "stump" me. This activity could be tied into lessons on powers of two or even binary numbers.

Survivor

2009-12-20T20:35:00.000-06:00

Every teacher has those short, time filler activities to use for various reasons. I will spend my next few posts sharing some that I do because you really can only use them a few times before they lose their luster, and I'm sure some teachers are looking for more.

Survivor
Objective: To be the last person standing at the end of the game.

Materials: Every person, including the teacher, needs a number cube or die. I like to use the die on the SMART Board for mine.

Rules:
1. Every student stands up, then rolls their die.
2. Once the teacher sees that all the students have rolled, the teacher rolls his/her die. Any student that has a number that matches the teacher is eliminated and sits down. For dramatic effect, I like to say "The tribe has spoken."
3. Steps 1 and 2 are repeated, but only with the students who are still standing.

The game is quick and easy. I give out a mini prize to the winners. The probability ideas could be worked into a lesson as well.

Careers in Math Glogs

2009-12-05T17:28:00.000-06:00

I recently had a few of my students do a mini-project using Glogster. They researched careers that have math backgrounds on the "When Will I Use Math?" website. From there, they used the important information to create their own Glog.

Here is a link to a larger version of this glog, as well as a few others that were created - another biologist, statistician, attorney, and physician.

Accelerating Students Follow Up

2009-12-04T21:59:00.001-06:00

Just a follow up on my post about accelerating students from earlier in the school year. Last year my advanced 7th graders had to basically teach themselves concepts from the 8th grade book. I'm totally against it, but it was the situation I walked into. This year those students, along with a few others, are now in Algebra I. Today we talked about the Pythagorean Theorem.

At the beginning of the lesson, I heard a comment, "Oh great, I didn't understand this at all last year. This is not going to be fun."

At the end of the lesson, I heard, "I actually get it this year. It's actually kind of easy."

Music and Learning Math

2009-11-29T19:20:00.003-06:00

It's no doubt that people can remember information better if the information is sung to a tune. Using music in class is such a great tool, but it can be hard for some teachers to create songs because they are not musically inclined (such as myself). I think it would be great to create a compilation of math related songs that teachers have used to help their students learn concepts. I will get started with a few that I have used or plan to use:

Adding Integers Song (sung to the tune of "Row, Row, Row Your Boat")
Same signs - add and keep
Different signs - subtract
Take the sign of the higher number
And then you'll be exact!

The Pi Song performed by The Derivatives. The song is sung to the tune of 867-5309/Jenny. Here's the mp3 download of the song I use.

Fraction Rap by Mr. Duey

Sean Sweeny's Slope Rap sung to the tune of Flo Rida's "Low"

Of course there is the ever-popular Schoolhouse Rock songs for learning multiplication facts.

"What You Know About Math" sung to the tune of T.I.'s "What You Know" - Original Version and Middle School Version. Not really useful for learning specific concepts, but they are good for showing when you have 5 minutes to fill.

What are some songs that you have used in your math class? If we can get enough suggestions, I will start a wiki to build our resources!

Indiana Standards and Resources

2009-11-12T19:25:00.000-06:00

For anyone working on refining their curriculum, I was introduced to an excellent resource. The Indiana Department of Education has a standards search engine that provides assessments, activities, and lesson plans that go along with each standard. To find these, search for math standards at your specific grade level, expand each standard, then click "View Resources." The classroom assessments are particularly useful for doing backwards design lesson plans.

Explaining Thought Processes

2009-10-30T13:47:00.000-05:00

My students will begin taking the standardized state test for math next week and I thought I would share something that I do with my students to not only prepare them for certain types of questions on the test, but to give them a skill that they will need to use for the rest of their lives.

Our state tests have 2-3 constructed response problems that our students need to solve. They are given a problem of elevated difficulty and they are expected to find the answer and describe how and why they came to their solution (see question #11 or #18 on this sample test). The students in my district typically do very well on the state test, but these types of problems are the ones that seem to give them troubles.

I decided to attack this problem last year. Describing your thought process or explaining why something is correct is hard for students to do, especially if they've never had to do it before. I don't think I ever had to explain my thought process in words until I got to college, and even then I struggled at the beginning. I could do it verbally, but putting those thoughts on paper was just something that was not normally done.

To start the lesson, I discuss with my students about why it is important to be able to explain your answer to a story problem. They need to know why it is important to do this in order for them to buy into this process (and not just for the test either). This year, I gave them the example that President Obama is trying to solve the problem of finding a way for universal health care to work in our economy. If he comes up with a solution, some people may not understand all the details behind his solution. As a result, he needs to be able to effectively communicate his ideas so that everyone can understand his solution.

After that, I ask my students about what makes a good solution to a short answer problem. The ideas my students come up with can be simplified to two main ideas:

1. Use the 6 traits of writing
Our district is big on the 6 traits of writing. Since the solutions to short answer problems involve writing, I feel the 6 traits should also be included. I try to be a little more specific by telling my students to use complete sentences, proper vocabulary, sentence fluency, and labels. I think the question should be restated within the first few sentences of your answer.

Instead of an answer that says "I timesed 6 by 8 to get 48," (which used to be a common answer) I tell them a much better answer would be "To find the area of a rectangle, you multiply the length by width. Since the length is 8 feet and the width is 6 feet, the answer is 48 square feet because 6x8=48." Notice how you can figure out what the question is based on my solution without even seeing the actual question.

One thing that I tell my students is "If you make it sound like you know what you are talking about, even if you don't, chances are you will impress the reader enough to give you a higher score." They seem to buy into that pretty well.

2. Explain your thinking
This is definitely the hardest part for students to do, but as teachers, you have to coach them on how to do this. Like I stated before, many of them could describe the process of getting an answer verbally, but they just don't get how to do it in writing.

In explaining your thinking, this is where sentence fluency helps. I tell them to just describe their steps in order of how they solved it. For example, "First, I did this. Then I did this. Next I did this." Using those transitional words will really help to organize their thought process.

Just because the student describes the steps in order of how they solved it doesn't mean they understand what they are talking about. I also tell them to describe why they did a certain operation. If they said they added 5, 7, 12, and 3, I would want them to describe why they added these numbers. By doing this, it will solidify that they know the concept.

Sometimes I have students that will tell me they still don't know how to explain their answer. I can see they have a solution, but they don't know how to explain it. I will nonchalantly ask them what they did. I might toss in a "Why did you do that?" After they get done telling me, usually I can see they know what they are talking about. I then tell them, "Everything that you just told me, write that on paper." It's a simple strategy, but usually it works.

After we discuss these ideas, I feel it is important to immediately let them try a constructed response problem on their own. I give them a problem and let them work on what they think a good solution would be based on the ideas we just talked about. After 5-10 minutes, depending on the difficulty of the problem, they share answers. Other students and myself provide constructive criticism on their solutions. Modeling a good solution is also a great idea as the students can see what is expected of them.

Sometimes having a teacher generated response isn't the best idea because the students will downplay the expectations as the math teacher is supposed to be the smartest one in the room. Instead, show student responses that meet your expectations. The Massachusetts Comprehensive Assessment System website may be good resource for this as you can search for questions based on grade level, subject level, and question type. If you toggle the answers on, you can also see sample responses from students.

I spent about a one class period going over these expectations, but I also have them practice periodically throughout the year and continue to model good solutions.

Too Much Help?

2009-10-24T09:32:00.000-05:00

The day before my students take a test, they complete a study guide of problems that are similar to ones that may be on the test. I also allow them to add any other notes to the study guide if they feel it is necessary. Most students do not add any extra notes; they just complete the problems and are satisfied with that. I allow these study guides to be used as an aid on the test.

I picked this idea up from my former cooperating teacher during student teaching. I was a little unsure of the idea because I hardly ever had this opportunity when I was a student. If I was ever allowed to use a "cheat sheet", I took full advantage of it and was almost certainly guaranteed an A.

I'm not sure if I am doing the right thing by allowing my students to use these study guides. On the one hand, I think it calms the sense of test anxiety that some students have as they can always refer back to their study guide. I also have some students rewrite example problems and definitions on their study guides which I believe helps reinforce their understanding of the concept. I used to rewrite my notes in college the day before a test to help remember concepts, so why wouldn't it work for my students?

On the other hand, I feel I may be setting my students up for failure down the road. Their high school teachers and college professors will not allow them to use study guides.

Although I allow these study guides to be used during the test, I don't feel that the use of them has ever greatly affected the outcome of their grades. At times, I still have students that will perform poorly on tests. My thinking is that if the student hasn't become proficient in a concept by test time, the study guide will not help them. I still think the benefits (reduce anxiety) outweigh the detriments (too much help). What do you think?

Qualities of a Good Math Teacher

2009-09-07T18:20:00.003-05:00

Like several other math teachers on the first day of school, I handed out a modified version of Dan Meyer's Who I Am sheet. I like having the students do things like these because I get a chance to learn more about the "real-lives" of the students. They also get a chance to be a little silly. Or they might write down more information than they might care to share while talking face-to-face with you. For example, I had one student write "I have never kissed a boy (don't tell anyone)." I guess I didn't follow her orders so I hope none of her friends read this.

One of the statements that I was anxious to read was the responses to qualities of a good math teacher. Here are most of the responses:

smart/knows math well
funny
nice/kind
helps/knows when students need help
explains things well
listens well
able to answer questions
connects with students/gets to know students
strict when needed
easy or no homework
makes class interesting
patient

These responses seemed to repeat in every class that I read and many of them seemed to repeat with each paper that I read. The top three responses that I received were smart, funny, and explains things well. I think every new teacher should remember those things when you have a lesson that didn't go so well. If you can get the students to laugh, you can always correct your lesson the next day.

I went through my own answers to the sheet with my 8^th graders and it made me think about what my response would have been to the same question. It took me a while to think of something because I have a lot more perspective than a 12-14 year old.

It made me think of my favorite math teacher from 7^th grade. She was the only math teacher I had that I can remember that allowed for some sort of hands-on learning. I remember receiving a packet of artistic circles constructed with a compass and straightedge similar to these. I remember spending several hours at night exploring different ways to construct these shapes. It was so appealing to figure out a design all by myself without being told how to do it. Figuring out that a circle could be split into six equal parts by using the length of the radius may have been the most exciting thing to happen to me that year.

It made me think of my worst math teacher. Every day we sat through boring lectures and boring overhead transparencies. It made me not like math for a couple years. She was also the type of teacher that made no attempt to get to know the students. I actually ran into her at a math conference last spring. Not surprisingly, she couldn't remember who I was.

It made me think of my most favorite teacher. My 5^th grade teacher was by far the best I've ever had. She must have put so much time and effort into everything that she presented for us. I can still remember her making a silly sound effect after every three place values so that we knew where to put a comma in a number. I can still remember her demonstrating improper fractions by trying to put the largest kid in my class on the shoulders of the smallest kid. On a non-math note, I think I can still recite the Preamble to the Constitution because of her.

I also thought about a great college professor I had. She taught me the art of good questioning and the ability of teaching math without lecturing. I had never really experienced these things and she was able to model them so well. The thing that amazed me was that she always acted like she never knew the answers to our problems (which is kind of ridiculous now that I think about it...she is a professor), but somehow she would get us to answer our own questions and pretend like she discovered the answer with us. Either that was the case, or she is some sort of genius. Sometimes when I am trying to create a lesson, I try to think "How would Jen teach this?"

It was really hard to put these four teachers into a few short phrases for my students. If you look back at the answers my students gave, I think all the teachers I mentioned fit the bill in one way or another. Hopefully I meet these characteristics as well.

On a humorous note, one student also mentioned that a quality of a good math teacher is being tall. So if you consider yourself short, you must not be a good math teacher :)

Thanks for reading!

Accelerated Students

2009-09-06T09:32:00.004-05:00

If there is one thing that frustrates me about the school district that I work for, it is how they handle the accelerated math students at the middle school level. There are a few different approaches that could be done to handle accelerated students and I think our district does the worst one. Here are the three most popular ways that I have seen:

1. If the student is working at an advanced grade level, that student is placed in a classroom with older students.

2. Keep the student in the classroom with students at his/her grade level, but differentiate instruction so that the student is appropriately challenged.

3. Keep the student in the classroom with students at his/her grade level, but they work independently in the book from the next grade level.

I have no problems with the first two methods. I understand that school districts have certain restrictions and may not be able to adjust schedules in order to move students up a grade level for one class, so method 2 would work just fine. However, method number 3 is the choice of my district. There are so many problems with this method that I don't even know where to start. First of all, for this method to work, the student needs to be an above average reader to understand the text from the book. They also need to have great study skills so that they can find key words and concepts that are important. Although some middle school students have an innate ability to do this, many do not.

The biggest problem with this method is that the students do not have a real "teacher." Of course, I am in the room to help when needed, but sometimes the questions come up when I am in the middle of a lesson and cannot attend to them right away. Since I have at least two accelerated students per class, I allow them to work and discuss problems with each other. This way, they can at least alleviate some of the stress that can come up when learning new math concepts on their own.

I'm not going to list all of the benefits or disadvantages to this method, but rather ask for opinions. I spent a lot of time last year trying to convince the administration not to do method 3. It did not work. How does your district handle accelerated students? What could I do to change their ways?

Thanks for reading!

School Year Resolutions

2009-08-24T12:43:00.002-05:00

Sam Shah has requested for resolutions for the new academic year with the following rules:

You should come up with at least 1 but at most 3 resolutions. This is so you don’t get overwhelmed.
They have to be easily doable and sustainable throughout the year. This is so you don’t get overwhelmed.
You need to publicly announce them – whether it be on your blog, on twitter, on the comments here. This is so you have some external accountability.

I would hope that every teacher does something like this every year, at least mentally, to make themselves a better teacher. I had a few things in mind that I already have worked on within the last few weeks. Here are my resolutions:

Allow my students more opportunities to be rewarded for doing a "good job." I am going to do something similar to a Student of the Week. I have based it off of the idea that I found here (see #1). This was something I have wanted to do for a while, but two schools in two years helped me push this to the back-burner. Rewarding my students with my excellent humor just wasn't good enough in my eyes. Hopefully this reward will give them a little something extra to work towards.
Present more information on how the math that is being learned is used in the real-world. I felt that I did this well in my first year of teaching. Last year, not so much. I do a project with my 8th graders on the cost of living (which I hope to share after it is completed this year), but I feel that I need to answer the question "When are we ever going to use this?" more often. These websites will definitely help me out: When Will I Use Math? and The Futures Channel. I've also had the idea of doing Skype interviews with professionals that use math in their jobs, but that may be a bit too adventurous for me.
Do not get overwhelmed. I will be wearing many different hats this year. In addition to trying to make my lessons better, I will be part of the building's Leadership Team, the Staff Tech Support person, 7th grade football coach, and probably a baseball coach of some sort. Don't forget the math curriculum and benchmarks that have to be tweaked. I just have to remember to be very organized (which I consider myself to be) and take the necessary breaks when I need them.

I think these are two very manageable things to do as well as one very important reminder. I have no doubt in my mind that I will be able to follow these resolutions.

Thanks for reading!

Using a Wiki in Math Class

2009-08-21T22:19:00.004-05:00

Near the end of one of the chapters in my algebra class, I felt my students needed some extra reviewing to boost their confidence and understanding of multiplying and factoring polynomials. Earlier in the school year, I found Darren Kuropatwa's AP Calculus Solutions Manual and thought it was an excellent way to review and to integrate technology.

This was going to be my first wiki and my original intent was to try the wiki module in Moodle. However, the equation editor that had been installed in Moodle had some sort of security risk and had been uninstalled and unusable. There goes that idea.

Plan B: I spent some extra time learning the ins and outs of PBworks to replicate Darren's wiki. I used the LaTeX Equation Editor by SITMO, which was handy because it could be embedded on the side of the wiki.

I basically used the same directions as Darren, with the exception of a few modifications. I chose two problems from each lesson of the chapter and assigned each student a problem to solve. I chose problems that were above average in difficulty.

Here is the link to the Algebra Wiki from my class.

The class spent around three days working on this project. The first two days were used to solve the problem and construct an answer. The last day was used to review and comment on other problems.

Overall, my students and myself liked this project a lot. We spent all three days in the computer lab working on the wiki. I'm assuming Darren had his students complete his wiki outside of class, so my students didn't get to truly collaborate across an online environment, especially when some of them did their collaborating face-to-face during class. However, I don't think my students would have embraced this project if I handed them sheets of paper with the problems and told them to complete them. Technology is not only something that I am interested in, it is something they are interested in as well.

One downfall to this project was was the LaTeX Equation Editor. My students frequently complained how it was not very easy to use. If they made a mistake with their equation, it wasn't very easy to edit. In the end, it became too time consuming for them to use. I plan on doing this project again, but I will be using Moodle this time around. The equation editor I have in Moodle is similar to MathType that can be used in Word and will be much easier to manipulate.

Thanks for reading!

Homework Policy

2009-08-18T12:26:00.004-05:00

There are many arguments about whether math teachers should assign homework, and if they do, how much to assign. I'm not here to argue about these things, but to simply state how I handle homework in my classroom since I missed the boat on this survey.

I assign about 10-15 problems almost every day. On most days, my students get enough time in class to get most of these problems done. Technically, they only have around 5 "homework" problems to complete.

I do not put a lot of weight on these assignments as they are just practice. For some of the students, they are practicing newly learned concepts and could have a little trouble when they try them on their own. As a result, I grade the assignments on a four-point scale. I'm not sure if I completely like this idea yet, but it seemed to work really well last year.

1 point for getting the assignment done on time.
1 point for attempting all the problems: Nothing irks me more than a big question mark next to a problem. I stress that I would like for them to at least attempt a problem, even if their solution is way off base.
1 point for showing all work: I tell them that if the problem involves a calculation, then work needs to be shown.
1 point for receiving 80% accuracy: If students get below 80%, they can make corrections to the problems that they got wrong and turn them in the next day for full credit.

The answers are posted on the SMART Board when the students walk in the room and they immediately begin grading. I have a spreadsheet that I use to quickly walk around the room and collect scores. After I collect the scores, I answer any questions. I found this method to be very quick as it only takes up about 5 minutes of class time.

I am going to try a small incentive this year for my homework. I am going to give each of my students one of these business card-size passes per semester.
I decided that I needed to have more incentives in my classroom this year, and this was one of the ideas that I came up with. It's not really that much of an incentive when you think about how much homework assignments are worth, but to a student, this could be very valuable.

I am pretty happy with my homework policy right now because it is very efficient and I don't spend 15 minutes correcting the problems and another hour every night putting the scores in the gradebook. I think my four-point scale may need some tweaking, but it has worked out well in the time that I have used it.

Thanks for reading!

How I Use Moodle

2009-08-11T12:45:00.016-05:00

Moodle is a course management system that allows educators to create websites, forums, quizzes, online assignments, and many other things for their students. As a new teacher to my district last year, I didn't start using Moodle until late November. It was very overwhelming for me at first because there are so many features, but I had a few ideas on how I wanted to use it and I played around with the Moodle Demonstration Site to fine-tune my ideas.

Since many Moodle class sites are set as private, I decided that I would share some of the ways that I use Moodle and hopefully I can receive a few other ideas from my readers.

Moodle can be used to create websites. I use it to post important links that can be used at home for a variety of things.
Individual links to websites can be created. Our algebra textbook has web codes that can access lessons quizzes, chapter tests, and videos. Instead of having the students enter these codes, I have provided direct links to these resources.
Our student-created Mathcasts are embedded from SchoolTube.
Links to math games are posted by embedding a Glog.
I also use the website feature to post the weekly lesson plans and homework assignments.
Our school received a grant to help improve our students' ability to solve story problems using constructed response. I created online assignments to have students practice their constructed responses. I was able to grade these responses in Moodle and give feedback if necessary.
I created an end of the year assessment using the ExamView software that was provided with our textbooks and imported the questions into Moodle. The test was also graded for me, saving me the time spend grading.
One of my favorite features that I use in Moodle is the forums tool. I created a Homework Help Forum for my students to use at home if they have any questions that their parents can't answer. My algebra students utilized the forum a lot more than I was expecting. During the upcoming year, I am really going to make a push that my students take advantage of this extra help.
I have a SMART Board in my classroom. After a class is over, I can save the notes as pdf files. I am planning on uploading these files to Moodle so that all my students have access to the notes if they are absent or maybe want to review a concept after class.

Moodle is really a great resource for students and teachers. I really hope my students take full advantage of all the tools available to them. If you use Moodle and have another idea that you would like to share, please leave a comment. Additionally, if you want more details on some of these activities, don't hesitate to ask.

Thanks for reading!

Math Games Glog

2009-08-08T16:50:00.009-05:00

During summer school, I taught a class called Math Games That Teach for students going into 3^rd through 8^th grade. I was lucky to have a computer lab for this class, so many of the games that we played were online. Here is a Glog that I made that contains links to all the games that my students played. I think Bloxorz was a class favorite.

Here's a link to the larger version. I would like to use Glogster during the school year to create some mathematical Glogs, but I haven't seen any good examples of math Glogs.

Thanks for reading!

Reflections on Mathcast Project Part 2

2009-08-08T16:30:00.004-05:00

My second run with Mathcasts was an end of the year project with my 6^th and 7^th grade students. A few modifications were done this time around: students worked individually, they had more practice time, and recordings were done during class. I decided to have the students work individually because I received an AirLiner graphics tablet and felt it would be easier for the student to do the writing and talking by themselves rather than rely on the timing of a partner. Here are a few examples of the videos these students created.

You may notice that the format of these videos is slightly different than the videos my algebra students created. After getting a chance to view all the videos, I was not as pleased with the outcomes as I was with the algebra videos. As a result, I edited the videos that were posted to only include an example problem. These were two of the better Mathcasts out of approximately 50 videos.

I allowed the students to choose any topic that was taught during the year and I gave them several chances to practice their presentation. So why did my younger students not meet my expectations as much as my older students did? Maybe my expectations were too high in that my algebra students were all advanced and generally did an excellent job on anything that I assigned. This project was also completed in the last two weeks of the school year. Most of the students are concentrating on how they will celebrate the evening in the warm weather rather than worrying about how to properly describe the steps to finding the area of a trapezoid. I also think that having students work individually on this project slightly affected the outcomes. I was most disappointed in the narration of the videos and I think that having two students work together helps to create a rock-solid script.

I still plan on doing this project during the upcoming school year, with some additional modifications. I think that I will always have students work in partners for the reasons mentioned above. I also plan on spreading out the recording times will help keep my own sanity. I had about a week and a half time period to get 50 students to record their Mathcasts during school. I needed to use class time, lunch time, study halls, and even the help from one of my colleagues to switch classes with me so that I could get the students to finish. It was definitely very stressful.

If you have any other suggestions on what could be done differently for the younger students, leave a comment.

Thanks for reading!

Reflections on Mathcast Project Part 1

2009-08-06T11:29:00.009-05:00

Let me dive into the blogging world by reflecting on a project that my middle school students worked on last year. On two separate occasions during the year, my students created math screencasts (Mathcasts). Mathcasts are an excellent project for students to work on because the student really has to understand a concept in order to teach it to the audience. Thus their retention of the concept will be much longer than that of learning by reading or by listening. I was first inspired by the idea after seeing Tim Fahlberg’s website. The publisher of our algebra textbook also has several videos aimed at helping students with their homework.

Not knowing how it would turn out, I tried this project on my 8th grade algebra students. These students were eager learners and would be willing to adapt to changes if a problem arose. Students worked with a partner to complete the project; one person was the speaker and one person was the scribe. I decided that this should be a partner project because we had just finished a difficult chapter on systems of equations and inequalities and I felt that they would be more confident in coming up with the proper vocabulary and explanations if they could bounce their ideas off of a partner. I also was limited with my resources in that my SMART Board was located in the front of the room while my computer with the microphone was located in the back of the room.

After students received the guidelines of the project and viewed a couple sample videos from the Prentice Hall website, each group picked their topic. They were given about 60 minutes of class time to figure out what problems to teach, what vocabulary to use, and the proper way to present these ideas. After that the students received two class periods in the computer lab creating their slides and writing the script. The slides were created using PowerPoint with the aid of the equation editor. I would have loved to use SMART Notebook for the slides, but this wasn’t an option as only four computers in our building had this software installed. Another class period was given to students to practice their presentation and get used to the different features of the SMART Board. Students came in during their lunch hour to do the actual recording of their videos. Here are a few of the results.

I was very happy with the results of this project. There are a few mathematical errors on some of the videos, but looking at the big picture, the students met all my expectations.

Please leave some constructive criticism or some feedback on how you have done your Mathcasts. I will reflect on the second time that my students completed the Mathcast project later. Thanks for reading!