A New Diagnostic

Students often come into grade 9 faced with a number of transition challenges (I previously wrote about these here).

Teachers, too, face challenges in preparing to teach grade 9 math, not the least of which is determining the skill level of students coming from a variety of backgrounds and experiences, all with different identified strengths and needs.

The more information we can gather about our students, the better we can serve them. As our team of math co-ordinators works with teachers to determine how we can help our grade 9 students that need the most help, there is always a lot of talk of determining benchmarks in math.


With respect to math skills, at what level are our students now? 
Where do we want them to be? 
And then how can we get them there?

This year, we decided to design a new diagnostic assessment to compliment the existing EduGAINS gap closing resources, and help us mark those initial benchmarks, as well as help us measure growth over time.


Where to start?

Based on conversations with grade 9 math teachers in our board, we chose four critical Big Idea Trajectories in Mathematics to test: Proportional Reasoning; Patterning into Linear Relations; Operational Sense (Number Sense & Algebra), and Operational Sense (Basic Computations).

For each of these trajectories, we started with the grade 9 applied (MFM1P) curriculum expectation, and worked backward through the curriculum to grade 3, in order to create a continuum of learning.

Even though a student in grade 9 is not expected to have mastered the grade 9 expectation, we decided to include it in our continuum (and assessment) because we are not just looking to see where students get stuck, but we also want to identify students who are perhaps working above potential, so we can devise strategies to best engage them as well.

**Note: since the diagnostic was created, we found grade 10 teachers wanted to be able to use the resource to create benchmarks as well. We added the corresponding grade 10 applied (MFM2P) strands and questions, as seen below.


A sample continuum from our teachers' guide to the diagnostic

Then, with each of the curriculum expectations, we created questions for the diagnostic assessment. As much as possible, we used wording and sample problems directly from the curriculum documents. For the grade 6 and grade 9 applied questions, we used released problems from past EQAO assessments.


Grade 4 through grade 10 applied questions, matching curriculum expectations for proportional reasoning.


Ideally, students work through the continua of questions to the best of their ability (the test does not identify each question's level). It was our hope that because of the nature of the continuum, we would be able to see at what level each student gets "stuck."


A First Run

After trying the assessment with a number of different classes this September, we've learned quite a lot about our students, as well as about our assessment itself!

Changes we've made through implementation:
  • Initially, we had all questions in one large test, but that was too overwhelming for students. We then broke the test into five sections based on the trajectories represented. 
    • Solution: We encouraged teachers to give the students one test per day to break it up, or even spread out the diagnostics throughout the course, using them as assessment for learning coming into new topics.
  • Originally, we placed the proportional reasoning and patterning and algebra questions ahead of the computations. For teachers who did want to do the entire test in one go, we found students who struggle with reading and decoding word problems grew tired and frustrated early on, and just chose to leave the rest of the test blank without even trying.
    • Solution: We suggested to teachers to either break up the test (above), or at least give the computational questions first, ahead of the proportional reasoning and patterning and algebra sections.
  • We found that some students would get stuck (and frustrated) when attempting questions above their grade level. We saw some grade 7 students get incredibly frustrated that they couldn't complete all the questions
    • Solution: We recommended to teachers that they remove any above-grade level questions for students they feel might be discouraged.

New learnings for teachers:
  • Some grade 9 teachers were not aware of how their grade 9 curriculum tracked back through earlier grades - this was an eye-opener to them as to when students first see certain concepts.
  • Some of the best learning for teachers came as they watched their students write the test, and not how what they achieved on the test: how did the students respond to a challenge? How much did they persevere? What strategies did they use?

Next steps:
  • As the first iteration of teachers use this test with their students, we are collecting examples of student solutions. Our hope is to make a bank of exemplar solutions that highlight multiple ways of thinking.
  • Once the diagnostic is used to help set benchmarks, we want to work on tools or resources that can be provided for teachers to help them track progress and measure growth.

What diagnostic tool do you use for your math classes? What parts of a diagnostic tool do you feel is the most useful to you as a teacher?

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