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.)

Problem Solving in Kindergarten

In Gwen's kindergarten class they have been talking a lot about the weather - And the topic of rain clouds and rain drops came up. Gwen used this discussion to have her kindergarten children participate in a Parallel Task.

The children were given a drawing of a rain cloud. They could choose between one rain cloud or two (this is what makes the task parallel). Once they had made their choice the students then rolled the number cube to determine how many raindrops the cloud would have. They wrote the number, and drew the rain drops.

From this activity, Gwen met many different Kindergarten math expectations:

Process Expectations:

* Problem Solving, Connecting, Representing and communicating;

Overall Expectations:

* Demonstrtate an understanding of number, using concrete materials to explore and investigate counting, quantity, and number relationships; and

Specific Expectations:

* Investigate some concepts of quantity through identifying and comparing sets with more, fewer, or the same number of objects;

* Recognize some quantities without having to count, using a variety of tools or strategies;

* Use, read, and represent whole numbers to 10 in a variety of meaningful contexts; and

* Begin to make use of one-to-one correspondence in counting objects and matching groups of objects.

In addition to this, Gwen was given a great assessment opportunity as she could then make observations about her students knowledge of number. For example, she could see who was able to print numbers correctly, who could demonstrate one-to-one correspondence, who could show synchrony (assigning one word for every object), and who can use the 1-9 sequence when counting (stable order principle) and cardinality. As well, she was able to see who can self correct when they make a mistake.

Problem solving can be done in kindergarten - And when it is, the results are amazing!

Thanks for sharing Gwen!

Assessing For Learning and Consolidation

Nancy and I have been doing a lot of co-teaching in her Grade 5/6 class. All of our co-teaching sessions have been focused around teaching through problem solving in a three part lesson. This past week we had the students work on a problem around conversion of fractions, decimals and percents. (Picture #3)

We used the Assessing for Learning tool(A for L) as a way to document not only what strategies the students used to solve the problem, but also what errors they make. What came to our attention was a rather large error which became the topic of our consolidation or the third part of our lesson. (Pictures # 1 & 2) Nancy has also modified the A for L tool to meet her needs by making the squares a bit bigger, and also including a box for her to level the students work as well. (Not every time that we use the A for L sheet do we give the students a level - it is mainly used to simply assess for learning)

The students were quite easily able to figure out 1/4 of an amount and then find out what 50% of the remaining amount was. We saw several strategies and heard several different explanations as to how they got through steps one and two. However, where the misconception occurred was when the students got to the part of the question where they had to solve for 0.3.

The students were well aware of how to convert the decimal into a fraction - Except that they were trying to convert this particular decimal into 1/3 which then would give them the wrong answer. Many of the students said that they didn't know what to do when it came time to "deal" with the 0.30. For some that were stuck, we prompted them with open ended questions to them to help make sense of what they should do next.

During our consolidation piece we had one pair come up and share their work with the group. We had pre-selected this pair because we knew they had used the same strategy as most of their peers, and had made the same mistake. As they explained their answer I annotated what was missing from their words and their sheet by using a different coloured marker. When we came to the part about the 0.3 we had them share their answer and asked the class if this looked right. Almost everyone agreed. We then led the students into looking back on the first two questions they solved using the fraction and the percent. We put each one of those into a decimal, percent and fraction form on the board beside of us. We then did the same with 0.3, 30% and then 1/3. It was at this point that a few of the students got the "light bulb" look and put up their hands. They said that 1/3 was not equal to 0.3 but it was 0.33 instead. We then used number lines to help us show the difference between 0.3 and 0.33.

One other group - who were the only ones to correctly get the answer in the first place - put up their hands to share (and show us) how they solved for 0.3 and what it would look like in the context of the problem.

Had we not been doing this problem, this issue might never have come up. The three part lesson is a really powerful tool to help us teach our students better - It allows us the chance to take a simple, and easily corrected, mistake and fix it on the spot. Because of the consolidation piece (or congress) we were able to not only show our students different ways to show a number as a decimal, a fraction and a percent, but also stop them from making the same mistake later on.