One Question, Multiple Strategies

I've spoken before on the importance of teaching through problem solving, and how it truly benefits the students as it allows them to make meaning from the math, rather than us telling them what to do.  In Paul's Grade 6 class we co-taught a lesson on number patterns. This three part lesson gave us a great understanding of where the kids were at, and where we could take them next.


We began by completing a KWC -P chart with the class.  The "P" stands for plan.  We chose to add this to our regular KWC because he was finding that his students were very reluctant to get started on any type of activity, and thought that if they had some pre-discussion on what to do, they may be more independent and more successful.

As the students were working on their problem (in pairs) Paul went around and visited each pair and probed them on their thinking and ideas.  I worked with one pair a little more closely to help make sure that they were on task, and focused.  We used the assessment for learning tool (A4L) to keep track of what strategies the students were using.  Originally, we thought that they would use one of five strategies.  However, we added a sixth strategy as one group used a strategy we hadn't thought of.










We chose three different groups to share their solutions with the class as part of our whole class consolidation.  One group had the right answer, but didn't have a complete solution as I don't think they picked 13x8 = 104 on their first try!  As the group was telling us what they did, I filled in the blanks for them by using a different colour marker.  We called this "editing."  You can see samples of it below in some of the pictures.

The second group was the pair that I was working with.  We chose to have them share for multiple reasons.  One of the reasons was to build their confidence.  Both students are currently on an IEP and need a chance to participate and show their strategy.  A second reason was that they had put a lot of depth and thought into their answer and gave not only the answer, but a suggestion as to what the leftover money could be saved for.

The third group really blew our minds.  They got an answer of 7.7  At first, I thought they were way off base, but when I began to ask some questions about how the 7.7 came into play, a lot of knowledge and understanding came into play.  The 0.7 of the lawn was because the student has a dog.  Her mom doesn't cut all of the grass each time she mows because the dog likes to have longer grass to play in.  Therefore, if the student mowed her mom's lawn she wouldn't charge the full price for the lawn mowing.   She would only charge 0.7 of what her regular cost is. 

We then had the rest of the groups come and put their work up on the board in a Bansho format.  In total, we ended up with 6 different strategies that were used to solve this problem.  So much richer and more meaningful than us showing the students 1 strategy and making them use it.

Welcome Back!!!!

Welcome Back to the 2010 - 2011 School Year!

During the second last week of August I was lucky enough to be a part of Math E Motion - A week long camp for teachers and students (in Grades 6-9) which focused on teaching and learning through problem solving.  The culminating activity for the students was a hands on project that was based on a math problem they had chosen earlier on in the week.  The students picked "Under The Sea" as the theme for all of their projects.  They showed these problems to their peers, parents and friends at an afternoon long "Math Fair."

Over the course of the 5 days, they worked together in partners to take the problem off the paper and make it come to life.  In total there were 18 different projects.  Each pair had different strengths and weaknesses, and each pair was also working at different academic levels.  The end results were nothing short of spectacular!  The students really worked hard, and put forth some excellent work.  Should the program run again next summer, I highly recommend participating in it.  You will be glad that you did.  If you want to run a "Math Fair" in your school, or have questions about it, please let me know.  I'd love to work with you to make one happen!



This problem was finding out the minimum number of moves you needed to make to cut off the dragon's heads and tails - For if you made one cut, one or two more things could grow.

Probability and logical reasoning are at the heart of this activity where you had to guess which box had 2 blue balloons, 2 pink balloons and 1 blue and 1 pink balloon.

For this game you have to place the numbers 1-8 in a row to find out what the greatest possible sum could be for each row.

Welcome To Kindergarten Night

This past week I was invited to be a part of General Crerar's Welcome to Kindergarten night. The principal (Heather) and the kindergarten teacher (Chris) had set up several stations for parents to visit. These stations were: Math, Public Health, Toronto Public Library, and a Teacher station where Chris had some activities set up for them to do with her.

The math station consisted of two games for parents to play with their children: Part, part whole bingo and a shake and spill game using the 10 frame mat.

 
 
Each child also got a "math goodie bag" which had the two games in it, plus a few other math items for them to use at home.  The bags cost under $1 per child, and were made up of items that were purchased at a local dollar store.  The items in the bag were:  A deck of cards, 10 two sided counters, a large die, stickers, part-part-whole bingo game, a ten frame, a piece of sewing elastic (to make shapes with) tangram puzzles, and a piece of foam to make the tangrams with.
 

 It was great watching the parents and their children do math together.  As well, it gave me the chance to share some fun cooperative learning games with them, so they can help their child grow as mathematicians.  Great job Chris and Heather.  The night was a great success!

Congress and Assessment

In Lisa's Grade 4/5 class I was invited in to co-teach a lesson with her. Her school is doing a math pathway this term and her pre-assessment task is "The Checkerboard Problem." The question asks students how many squares are on an 8 x 8 checkerboard. We posed the question to the students, handed them checkerboard templates, and then set to work making notes on our Assessment for Learning (A for L) tool.

All of the students quickly got the answer of 64 - none of them got the correct answer of over 200.  But what amazed us was how many different strategies the students were able to use in order to come up with the correct answer.  Lisa had told them she wanted them to try to solve it in at least two ways.  Many of them were able to solve it in more ways than just that.

Many of the students shared their strategies with us.  We were able to see that the students had a lot of different strategies to call upon when solving a problem.  After they described what they did, we used a different colour marker to give that strategy a name that they could remember it by.  One key strategy was missing, so at the end of our congress I shared with them how to make a table to help them find an answer. 

When our congress was over, we then let them know that although they had really good strategies, none of them got the answer correct.  We told them that there are more than 200 squares on the checkerboard.  At first they looked at us with an "Are you kidding" face - But then one student piped up that she could see some of them that she hadn't before. 

The congress allowed us a chance to see what strategies the students already had in their schema, and then the A for L tool helped us see which ones were most commonly used.  At the end of the pathway, it will then be interesting to see if the students are still using the same strategies, or if new ones have become a part of their problem solving tool kit.

Student Success in an HSP Class

Karen's HSP class is composed of a variety of students, all at different levels of ability. She has been trying out problem solving in her class and has been surprised at the results. She has been encouraging the students to use a graphic organizer (seen above) to help her students comprehend what is being asked of them.

Karen is finding that the level of engagement her students have has increased since they started doing problems. As well, she admits that the first few times made her want to pull her hair out - But - now that the students have more schema to draw upon, they are achieving success and doing so independently.

The second picture shows some student samples from a problem that the class had done around fractions.

What is a Bansho?

Bansho is a High Yield strategy that you can use in your class with your students. It is used in Japan as a way to help students learn different processes in which they can solve a problem. Bansho literally comes from the Japanese word meaning "blackboard." In math, we use it as a way to display student solutions from the least to most mathematically rich. It is not about assessing the students work - It is about looking at solutions, annotating work and discussing solutions.

The above Bansho was done at the FOS Transitions session. The teachers completed a problem in pairs and then we (the facilitators) organized their solutions. The organization of the solutions also involves some thought and discussion. As more samples came up, some were moved to different places along our Bansho. Once the solutions were organized, as a group we discussed them and put a label at the bottom of each one. On the far left we had identified the work as logical reasoning, to the far right we had graphing.

Bansho allows students the opportunity to see many different ways of solving a problem. It works best when your students are in an environment where the consolidation (or congress) is happening in your class. In fact, once your students are comfortable in consolidating their work you can then move onto doing a Bansho as consolidation.

You can learn more about a Bansho by visiting these websites:

www.lkdsb.net/Program/elementary/junior/OAME2007%20JapaneseBanshoHdt.pdf

(This one is a PowerPoint from the LNS - Lots of colour pictures)

http://www.eworkshop.on.ca/ - Grade 5 - Growing Weave Designs

www.criced.tsukuba.ac,jp/math/sympo_2006/takahashi.pdf

www.curriculum.org/secretariat/may2.shtml

(This is a video with not only a Bansho clip - but other High Yield strategies in Literacy and Numeracy as well)

Visual Data

We have all become aware at how important data has become in education. As part of our PLC time at Dorset Park we took a traditional data wall to a whole new level - We made it visual, and practical.

Our session began by doing moderated marking on our Pre-assessment activity. As the marking was underway, we began to select examples of student work that was from the four levels. The students names were removed, and then placed under the grade that they were in (and under the appropriate level). Once the moderated marking was done, we then added the percentage of students who were at each level for each grade.

As we were posting the work there were some great conversations happening. One of the benefits to doing this kind of data wall is that since all of the teachers are doing the same concept (fractions) they are able to talk about strategies and teaching points that they have found successful. In addition, you can see similarities and differences between the levels, and gain a better understanding of what the students can do to improve.

Having it up allows for the conversations to continue, and then grow. Our plan is to put the culminating task activities (in the four levels) beside the Pre-assessment so we can see the changes in how the students respond.

(Thank you to Ed for being in our picture.)