KSA #01 Contextual Variables · KSA #02 Alberta Structure · KSA #06 Planning · KSA #11 Assessment

Accountability and Assessment in Mathematics

A post from 20 November 2018

In our last unit my team planned a huge cross curricular project with our Humanities partners. Towards the end of the project, my one Math/Science colleague said to me, for the end of the unit I have a 50 question multiple choice test we can give. I asked him, “do we need to give this test? Why can’t we use the project, their class work and the discussions we’ve had with students to assess their understanding?”. His response, “we need to prepare them for the multiple choice, standardized tests, they will receive in the future. Also, this makes it easier for us to compare strengths and weaknesses.”

Looking at another chapter in Keitel & Kilpatrick (1999), Romberg (1998) discusses the NCTM’s 5 Curriculum and Evaluation Standards for School Mathematics, which I think lend itself nicely to this discussion as well. Within these 5 standards, (1) Teaching math to all students; (2) More mathematics (students need to learn more than just manipulating arithmetic routines); (3) Different mathematics; (4) To learn mathematics means showing students more than just how to memorize and repeat; (5) Revised instruction implies that classrooms need to be communities of discourse, where students can make conjectures, present arguments and discuss their strategies.

To me, these 5 standards lend themselves to the cross-curricular project that engage our students in rich conversations and deep, meaningful thinking. The use of a 50 question multiple choice test, for the sake of comparison and practice for future standardized assessments doesn’t even come close. It’s clear that is influenced by these tests. This past month we were required to set our School Development Plan, and our targets are all related to report card stems and their corresponding PAT results. In addition to this, we had Parent Teacher Interviews this week. I often had conversations with parents about how their child was able to compute, but struggled to communicate their understanding in multiple ways, or explain why. I was often met with resistance and asked, “well, I’m old school, can you even explain to me why it’s necessary my child is able to do this? Why can’t they just give the answer?”. It’s difficult for teachers to progress their practice forward when the pressures from parents, standardized assessments and comparative studies are so heavily felt in our workplace.

On Friday, my colleague and I were talking about the Program of Studies with one of our student teachers. Keitel & Kilpatrick (1999) discuss “Curriculum as planned and as carried out”. Within the Alberta K-9 Mathematics Program of Studies there is a document that gives teachers the outcomes and achievement indicators attached. Our outcome for our fractions unit is, “students will demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially and symbolically”. Within the achievement indicators, order of operations is given as an example indicator. Looking at the actual outcome itself we engaged in a conversation and discussed how nowhere does it indicate that students should be able to solve fraction problems involving order of operations, so what are we to do? This brings to light the idea seen in Keitel & Kilpatrick (1999) of “Curriculum as planned and as carried out”. Looking at the planned curriculum (the outcome) we are unclear on how to carry out the work in our classroom and whether or not we will be able to do so in a way that is true to the intent of the specific outcome itself.

This made me wonder:

  • Do we need to teach fractions with order of operations as part of our ethical duty as teachers to complete the curriculum?
  • If we don’t (and assume we don’t have to) are we putting our students at a disadvantage?
    • For the record, yes I think this is something that is necessary to teach and by not doing so we would be putting our students at a disadvantage. These questions stem from the lack of clarity / detail in our guiding (curriculum) documents. Without the achievement indicators the mathematics program of studies would be very difficult to follow / ensure that we are meeting the intention of each outcome.
  • Finally, with the curriculum re-design happening now, is the curriculum document be written, free from ambiguity, so that all teachers can confidently say that they are effectively teaching their students the curriculum objectives as planned by the Alberta Government? Is this even possible?

Until next time,
Mr. B

Keitel, C. & Kilpatrick, J. (1999). The rationality and irrationality of international comparative studies. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 241–256). Philadelphia, PA: Falmer Press.

Romberg, T.A. (1999). School mathematics: The impact of international comparisons on national policy. In G. Kaiser, E. Luna, & I. Huntley (Eds.), International comparisons in mathematics education (pp. 189–199). Philadelphia, PA: Falmer Press.

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