Teaching Math in Authentic Contexts

Our staff recently has been examining the question: "What does math teaching and learning look like in a Primary Years Program (PYP)?"

To answer this question, we explored the text "Mathematics in the Primary Years Programme," one of the subject annexes from Making the PYP happen: A curriculum framework for international primary education. In that document, teachers were able to see the clear vision of how math teaching and learning should look like in our PYP.

To document their thinking, teachers created a Practice Profile (a rubric of teacher behavior) based on what they were reading in the text. As primary and intermediate teachers were working in separate sessions, there were two separate practice profiles created and can be found here: KEC PYP Math Practice Profile - Primary and Intermediate.

An important idea that came up during that professional learning engagement was that in a PYP classroom, teachers should provide students with multiple opportunities to explore relevant problems both inside and out of the units of inquiry. The math annex provides some guidance on concepts that might be best suited for learning in context when they say, "data handling, measurement, and shape and space are best studied in authentic contexts provided by the transdisciplinary units of inquiry," because they represent the "areas of mathematics that other disciplines use to research, describe, represent, and understand aspects of their domain," (p. 85 of Making the PYP Happen).

Reflecting on this new understanding of math instruction in the PYP, one G2 teacher planned for her students to create a timeline, an authentic opportunity to explore the abstract mathematical concepts of measurement, subtraction, space, and time. She knew that the timeline would give her students a better understanding of the heroes they were studying in their unit of inquiry, as they were trying to make sense of the big idea that people influence the world in different ways.

First, the students created the timeline using the scale 1 cm = 1 year. The students worked together to create century strips, each measuring a meter (and alternating in color).

Then, the students needed to figure out how long each of the heroes' strips should be. The teacher modeled how to use a number line to figure out the age of the hero they'd be researching. Using the birth date and death date (or the current date for living heroes), the students figured the difference between the two. It is important to mention that the students did pretty well with this since they have been using number lines and open number lines all year for almost every math topic. This shows how effective it is to give students the opportunity to use the same thinking tools and structures over and over again until they become routine.

Next, students used that information to create strips for each of their heroes, again with the scale 1 cm = 1 year.

Finally, the teacher gave students the opportunity to look at the timeline and document their observations, thoughts, and questions using the thinking routine See-Think-Wonder (from Making Thinking Visible by Ritchhart, Morrison, & Church).

This G2 teacher continues to see other ways that math can be learned in meaningful ways during her unit of inquiry. Recently, she used the data they had collected on heroes' ages to introduce median, mode and range. Using the data the students had already collected made it more authentic and engaging.

The students found that their heroes ranged in age from 37 to 95, a range of 58 years. Kids were surprised and impressed because that seemed like a lot. There were two medians and two modes, so that was confusing for their introduction to the idea of analyzing a data set using those tools, but it was engaging nonetheless.

After reading about how this G2 teacher taught the mathematical concepts of measurement, difference, and data in the authentic context of her unit of inquiry, how could you or have you taught math in meaningful, engaging and authentic ways?

Generate-Sort-Connect-Elaborate

On Friday, March 28, 2014, I wrote about how first grade students made their thinking about rocks visible using the Visible Thinking Routine "Generate-Sort-Connect-Elaborate" from the book Making Thinking Visible by Ritchhart, Church, and Morrison. Here is the story of how second graders used that same routine to make their thinking about heroes visible:

For the last several weeks in second grade, students have been investigating how people influence the world. They have been inquiring into the characteristics of a hero as well as particular people who have made a difference in the world.

Throughout the inquiry, students continuously generated a list of influential people as they read, listened, learned, and discussed different heroes.

Toward the end of the unit, as a way to synthesize all they had learned, their teacher led the students through a learning engagement where students had to sort the influential heroes into particular categories that the students created. Some of the categories the students thought of matched categories we all would think of, when thinking of heroes: inventors, scientists, presidents, writers.

The students also sorted their heroes into less-conventional groups: risk-takers and speakers.

As students were grouping the influential people about whom they had learned, they started forming a group that they couldn't name. As the students struggled to identify a singular word that would help identify the unifying characteristic that all the individuals in the group shared, they came up with the phrase "Treated Unfairly".

However there were some "heroes" that students were planning on putting in that group, who weren't treated unfairly. That phrase described some, but not all, so they still needed another group! Students continued to struggle to identify a singular word that would help name that particular group of people, although they knew that there was something special about this group; they were all good people, hard workers, who tried to make a difference for other people, other humans. At this point, the teacher intervened and introduced the word humanitarian to the students.

As the students sorted their heroes into the categories they had established, they quickly realized that certain influential people easily belonged in multiple categories. Their teacher suggested they add those individuals to as many groups as was necessary.

Then, the class connected those heroes who showed up in different categories. On the lines that they used to connect the heroes in the different groups, the students wrote character traits, which often were the PYP attitudes (e.g. independent, confident, creativity) and attributes of the IB International Learner Profile (e.g. knowledgeable, thinker, risk-taker).

Now that students had generated a list of influential people, sorted those individuals into groups the students identified, and made connections between the groups with character traits, the teacher could invite students to continue learning about other heroes that might fit into those categories (elaborate).

"What other presidents could we learn about?"

"Are there other risk-takers that influenced the world that we haven't learned about yet?"

"Where could we find more information on different humanitarians?"

This invitation to students to reflect on their learning and to choose how they'll continue learning will increase the likelihood that students will engage in thoughtful and appropriate action.

After reading about how 2nd graders made their thinking visible about the heroes they were studying, how could you or have you had your students make their thinking visible with the Visible Thinking Routine "Generate-Sort-Connect-Elaborate"?