why do we do this anyways?

I have never had a student ask me this in such forthright manner before...Why do we do this anyways?  We are never going to use this in our jobs.

Wow. From grade seven. I wonder what she will have to say as the mathematics she does at school becomes more abstract and seemingly disconnected from "real life".  Good for her to say how she feels and ask the tough questions. Although I wasn't expecting this today, I was prepared, am always prepared for how I might respond to this question.

Let me provide the context of this interaction...
I was at Quilchena Elementary for my monthly visit with the intermediate teachers. Today we focused on the role math materials/manipulatives can play in students' communication of their mathematical understanding and thinking.

We began our day in Una's grades 4 & 5 classroom working on using arrays to model multiplication and moving to using base ten blocks to model two-digit by two-digit multiplication with a focus on the place value language that "matched" the materials. This was hard work for these students. Many students were able to calculate the answers to the questions mentally and then modelled the answer with the base ten blocks. When re-directed to explain how this model showed the process of multiplication (which was the intention of the lesson), they were befuddled. The students needed some modelling and we used an approach to multiplication that could be described as distributed or parts-based and then connected this to the models that could be created with base ten blocks. There were some aha moments from students for sure but also, more work still to be done. Here are some examples of how the students worked through 12X23 and how some of the students represented the process in their math journals using pictures, numbers and words.

I moved on to Andrew's grade 7 class and worked through a similar process with the intention of moving to multiplication with decimal numbers. This is where the student's question came up as I moved from table to table. I took a few seconds to pause and calmly answered.

You probably won't use base ten blocks in any future job you have. You probably won't have to show your boss how you can multiply large numbers but...you will probably be asked to think, to problem-solve, to reason, to make sense of data and information. When we do things like this, it is to help you make meaning and create connections, to help you understand the mathematics more deeply, to be a thinker.

The principal takes all the intermediate classes for choir on the days that I visit so the teachers and I can meet together and discuss emerging issues in our collaborative inquiry. Today, we discussed students' notions of what math is, brain development, and why we teach math. Math isn't just for our students' future jobs. Being numerate is part of being an educated citizen who will make meaning of the world, ask questions and think critically. We talked about what mathematicians do...math is not about doing things quickly. Mathematicians spend long periods of time on one problem or proof, thinking, analyzing, synthesizing, generalizing, making conjectures, reasoning, creating models, etc. I think that sometimes we forget this in school mathematics which can often seem rushed and hurried to students.

After our collaborative time, I visited Tanya's grades 5 & 6 class that has been working on area and perimeter. With the resource teacher, I worked with a group of students on connecting arrays, area, perimeter, multiplication and division using colour tiles. Lots of oral explanations and mathematical vocabulary were used during our discussions.

For a performance-based task, the students in this class were designing their own apartments having to consider the total area and the area and perimeter of the rooms within. As I chatted with one student who had grandiose design ideas for her apartment, she said she liked doing this because it was real math, that she would use when she was grown-up. 

Made me think...sometimes the contexts and applications we provide in math classrooms help students to see the relevance of the math they are learning. Sometimes, it's not so clear and that's okay. We learn and think about math because it is developing us as thinkers and problem-solvers and nurtures the habits of mind that are going to help us in "real life" regardless of what job we might have.

~Janice

assessing mathematical communication

I made my monthly visit to Quilchena Elementary on Wednesday and the intermediate teachers and I worked together around assessing communicating about mathematics.

In Una Simpson's grades 4 and 5 class, the grade five students had been learning about quadrilaterals and their attributes while the grade 4s continued to develop their understanding of prisms. As a performance assessment task, Una designed a task where the grade four students would create a quadrilateral on a geoboard (real or virtual - on the Geoboard iPad app) and then the grade five students would ask their partners questions about the attributes of the quadrilateral that could be answered yes or no.

Una recorded some language prompts on the whiteboard such as angles, parallel, perpendicular, congruent, etc to support students' questioning. The students took a photo of their quadrilateral with the iPad and then inserted it into the ShowMe app and then recorded their question and answer session, with the grade five student trying to determine the size and shape of the quadrilateral.

What we quickly noticed is that although the grade 4 students could all create quadrilaterals, they didn't actually have the language for and understand the questions their classmates were asking them about the attributes. I listened with interest as a grade 4 student confidently say "yes" that there were parallel sides in her shape when there clearly was not. I pointed this out to the students and of course the grade 5 student was frustrated because it had thrown him off in trying to figure out the shape.

Una and I agreed that the task itself was excellent for assessing students' use of mathematical vocabulary and to assess understanding of attributes of shapes, but that students needed to be paired with students who had the same instruction and background knowledge for the task to be successful. So when teaching a combined class, if you do not expose all students to both sets of learning outcomes, you would need to separate this task by grade levels. The grade 4s could have easily have done a similar task but using prisms (using three dimensional blocks in the classroom) instead of the quadrilaterals.

*****

In Andrew Livingstone's grade 7 class, the students are accustomed to using self-assessments in other curricular areas, using a four point scale in line with our BC Performance Standards language. The intermediate teachers worked together to create a self-assessment scale to use with math journals, specifically focusing on communicating mathematical thinking. When we discussed it, we realized it could also be used with screencasting that the students have been doing with the iPads.

The students had already completed individual ShowMes using a practice question from the Grade 7 Numeracy FSA. A few students volunteered to share their ShowMes up on the big screen in front of the class so that we could use the self-assessment tool with them. I spent some time going through each level of criteria and what that might look and sound like in a ShowMe. We then shared the first ShowMe, with the students having the assessment tool in front of them. It was interesting to note that none of the students recorded anything on the assessment tool until after the ShowMe was over. I shared how I took notes during the ShowMe, so that I had "evidence" for my assessment for each level of criteria. The students soon realized that this would have been helpful. We discussed how they "scored" the ShowMe and asked for specific examples of why they chose "fully" or whatever level they chose.

For the second ShowMe we watched, the students took notes as they watched and had a better sense of what kinds of things they should be watching and listening for. They agreed the second time was easier than the first and that it would get easier the more they did it.

Here's a short little video from our session together:

With both examples, we had long discussions about the difference between "Show your work" and "Explain your thinking" building on previous discussion we have had with this class about descriptive vs explanatory thinking. For these tasks, the show your work was really about showing what you did to complete the task/how you did the calculations whereas the explain your thinking was the metacognitive part, the explaining the "why" you chose to solve it the way you did and your reasoning involved in completing the task. We are finding that we are really needed to pull this out of students, that they just do the reasoning part but aren't used to articulating it. We are going to make a few revisions to the assessment tool to help students understand these differences more clearly.

 ~Janice

Primary Scientists: looking closely at our practice

A large group of primary teachers in our district are taking part in the third year of Primary Scientists, a professional learning series focusing on process-based science and initially created as an implementation series to support the development of the Coast Metro Science Performance Standards. Teachers are all engaging in looking closely at one aspect of their practice in terms of science teaching and learning with an overall group focus of thinking about how we assess process and inquiry-based science experiences.

Using the science performance standards and assessment tools from the current K-7 Science IRP and the teacher resource book we are using for this series, teachers are asked to try different ways of assessing science performance tasks.

Teachers have chosen different aspects of science to focus on this year as part of their own inquiries into their professional practice: taking learning outdoors, looking closely (a national collaborative project), the processes of science, observational drawing and place-based learning using indigenous knowledge.

Based on the Looking Closely books by Frank Serafini, several of the teachers created their own versions of the books with their students. With her grade one class at Garden City, Jenna Loewen created a class book using garden photographs and having the students brainstorm what they could be.

April Chan at Blair took her students outside to look closely and create a peekaboo page with a hole cut out on the front page to take a peek at the illustration the students did of something they observed.

Sharon Baldrey and Kathleen Ellis from Lee Elementary looked closely at ice with their kindergarten classes. After freezing blue-dyed water into globes of ice, the students used salt and flashlights to investigate the properties of ice and how it melts. The teachers commented on how engaged the students were and what great inquiry questions came up during their investigations. Amazing photos of an amazing experience!

Louesa Byrne's K/1 class at Thompson looked closely at leaves in the fall and inspired by Ann Pelo's book, The Language of Art, observed and represented the leaves in using multiple forms of art materials - liquid watercolours, crayon rubbings, technical drawings with fine line markers and creating leaf forms with wire.

April Chan at Blair did a similar focused study of leaves with a small group of primary students. The students used the PicCollage app on the iPads to document the different ways they created representations of their leaves.

So as we engage our students in looking closely at the world around them, we too are looking closely at student learning in science.

-Janice

descriptive vs explanatory thinking in mathematics

On Wednesday morning, I made my monthly visit to Quilchena to take part in a collaborative inquiry with the intermediate teachers looking at alternative ways to assess students' mathematical thinking.

In Una Simpson's grades 4 and 5 class, the students had been studying various aspects of geometry. The day before I visited, Una listed a series of geometry-related topics on the board and pairs of students were assigned a topic to highlight in a "ShowMe" screencast. Students were asked to both describe the shapes they were using by their attributes and to explain the concepts involved such as what makes a prism a prism, what is a polygon, what is the relationship between two and three-dimensional shapes?

The students took several photographs that could be used to explain their topic.

And then used the ShowMe screencasting app to record their descriptions and explanations.

In Tanya Blumel's grades 5 and 6 class, we looked at the two types of division (sharing/partitive and grouping) and then the students worked through some three digit divided by one digit questions using the grouping method. As students shared their work, we focused on how they explained their thinking and the mathematical language they used to support their reasoning.

In Andrew Livingston's grade 7 class, the student have been learning about the relationship between fractions, decimal numbers and percentages. He gave the students a task from their textbook but instead of writing their responses in their math journals, the students were asked to explain their reasoning orally using the ShowMe app. The students coloured in the various shapes on the grid and then had to determine the fraction, decimal equivalent and percentage of the total grid for each space. The students' reasoning for the triangular shapes was the most interesting to listen to.

 This is ongoing work and we hope to see the benefits of focusing on oral explanations when we ask students to write about their thinking...hoping that the metacognitive writing will be easier for them with these background experiences.
~Janice

collaborative science inquiry at Blair

The primary teachers at Blair are taking part in a collaborative inquiry project looking at ways of moving science outdoors as well as ways of documenting science learning in science notebooks.
On Tuesday, I met with the teachers at lunch and then spent time in two classes in the afternoon.

In Tanyia Kusch's grades 2 and 3 class, the students have just begun learning about structures. The students could tell me what they had read about natural and human-made structures so we went for a short walk outside to notice some of these structures and to think about the question, What are structures?

The students then came back into their classroom to draw and label the structures they had seen outside, using their science journals.

As students were recording the structures in their journals, one student wondered, 

"Are people structures?"

The students enjoyed building structures using materials they found in the classroom. We had lots of portables, houses and a tree.

And a little animoto video:



In Karen Sato's grade 1 class, Karen started the class by reading Questions, Questions by Marcus Pfister to inspire the students to ask questions and wonder when we went for a walk outside. We walked around the school park looking for signs of winter.
The students found lots of mud, lots of moss and grass (such a mild winter we are having!) and some branches that had fallen to the ground during the latest storm.

We also found a large deciduous tree with an empty bird nest in. The students had lots of questions about the nest.

Why do birds live in nests?

Why is the tree bare?

How do they make nests?

Why are they are camouflaged?

Why do they make them with sticks?

Why do they only make nests in trees?

How does the nest balance on the tree?

We'll have to re-visit the tree in the spring and see if we see anything new!

~Janice