Saturday, March 18, 2017

When do they Learn That?

With the introduction of collaborative inquiry (CI) projects in our secondary schools this year, it's been very interesting to see what schools identify as their students' greatest learning needs, and choose how to address those needs.

For our Numeracy CI projects, many schools identified various aspects of communication as a significant need. It was interesting (but, some would argue, not surprising) to see evidence of this need from a number of different data sources, including past individual EQAO results, overall EQAO school trend results, student IEPs/psycho-educational assessments, and/or anecdotal information.

One school decided to look at vocabulary acquisition. How could explicitly teaching and placing emphasis on math vocabulary help students when it comes to problem solving?

Throughout the project, we explored different interventions for students, tried different strategies in class, examined student data, and listened to student voice. In the end, we were able to help a lot of students find success where they didn't experience success before.

But it's one of the spin-offs of this project that I wanted to mention and share.

When do they learn that?

During one of our team meetings, we were discussing which vocabulary words we expected students to know coming in to grade 9 math (and know well), and which words might be relatively new to students.

For instance, we figured students should know the word "area," since they start learning about the area of basic shapes in an early grade. However, the word "radius" is only introduced in grade 8 - having only been exposed to the word for one year, students might not yet have a solid grasp of its meaning.

(And, as an aside, a student who was on a modified curriculum before high school may not have seen the word "radius" at all. Important to note if we are now teaching these students in grade 9.)

But what about the word "angle?" 
Or "factor?" 
Or "ratio?" 
How well can we expect students to know these words?

A Vocabulary Continuum

We took a look at the glossary at the end of the Ontario Grade 1-8 Mathematics Curriculum, and the glossary at the end of the Ontario Grade 9-10 Mathematics Curriculum, and placed vocabulary terms in a continuum based on when they were first introduced. Check it out:

(scroll down to see the five strands, and across to see the different grades)

Being not familiar with the elementary curriculum at all until this year, I found this layout fascinating. I had no idea students learned fractions as early as grade 4/5 (many grade 9 students still struggle greatly with fractions), or that scatter plots - which I've always considered a "basic" skill in grade 9 - is a concept students would have only just learned in grade 8.

Some notes:

  • We chose to only look at the grade 9 & 10 applied stream (not the academic stream) to both keep the chart simple, and keep it aligned with our focus courses in the project.
  • In grades 9 & 10, the names of the strands change. We kept the same strands as in the elementary curriculum and tried to place the grade 9 & 10 words appropriately.
  • The placement of the words in the various grade levels was based on when they first appeared in the curriculum - this might actually be different in real life (and indeed, different from teacher to teacher, or from school to school).
  • As a spin-off of this spin-off, we also made a list of "tricky words" that have more than one definition - you can see those on the second tab at the bottom of the sheet.

What do you notice? 
What surprises you? 
How can this help when it's time to introduce new concepts?

Thank you so much to Kris Oliverio, Megan Parry-Jamieson, Iain Brodie, Randy Porter, and Richard Duffy for double-checking the placement of these words for me!

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