Since the beginning of this school year, I have spent more time than I would like to admit sorting, sifting and scouring over EQAO results, specifically Mathematics. Results were coded by correct/incorrect/missing or illegible answers, Level One, Two, Three or Four responses/scores, Open Response/Multiple Choice questions and even a question by question comparison of school score from (and above) provincial average. For a few nights all I saw were blobs of red, green, yellow, orange and blue when I closed my eyes.
Colourful dreams aside, with the results colour coded, we now had a great resource for beginning our work of analyzing/trend hunting through a rather large data set. Through a quick visual scan of the data, we were able to get a general sense of how our students performed across the strands, how they fared within each question skill (knowledge, thinking or application) and even how we performed question by question in direction comparison to the provincial average.
While we gleaned many things from our initial scans of the data, not surprisingly it wasn't until we dug a little deeper into some trends that we really started to notice things. Specifically we identified questions in which we scored 10 or more points below the provincial average as an area we wanted to look more into. We went through student responses and tallied how many answered A, B, C or D. We then printed out the booklets and went question by question looking at how our students scored and tried to identify what misconceptions and/misunderstandings that may have led to the incorrect responses.
Here are a few examples of what we saw:
46% of students answered C 31% of student answered B 42% of students answered ADo you notice any trends in the errors our students made?In looking a little closely at the errors, we determined that each error was actually correct math in one way or another.
Question 6: 800 metres multiplied by 50 minutes, but not converted to kilometres (bolded in question),
Question 7: 28 672 divided 5 times, but not recognized as the first term (which would only require 4 divisions)
Question 15: 365 days multiplied by 60 minutes (1 hour), but not by the full 24 hours in a day.
Now this shouldn't be a surprise as those EQAO tricksters always do their best to include misconcepted (new word? haha) math errors as answer options. But what drove our inquiry was our desire to understand WHY so many of our students were making these errors? Eventually we came to the conclusion that our students struggled to fully understand the requirements of each question due to errors in READING. Not reading errors in the sense that students cannot actually read the words, but in the sense that what was read was not understood. REAL READING (see Tanny McGregor). Having had an opportunity to examine data across multiple schools, I knew that this was a common error and not just specific to one school. We briefly talked about how we could address this issue, but nothing was decided as we were to meet again in the new year. In knowing that this was a growing concern for many schools, I began searching for resources that we could turn to for support in our attempt to address this issue. Unfortunately my search was going nowhere, until a book called "
Math Expressions" by Dr. Cathy Marks Krpan was mentioned during a professional learning session I attended just prior to the Christmas break. I had heard of this book a few years back from a colleague who raved about it, but never put forth any time to investigate it myself. What a mistake that was! I owe this colleague an apology...
I will start by saying that the entire book is an incredible resource. It is full of great research, assessment suggestions and strategies. For the purposes of this blog however, I would just like to focus in on a small part of Chapter 3 (Reading in Mathematics) specifically, as it targets what we feel our students are struggling with the most.
The chapter (like all chapters in the book) begins with a list called "Indicators of Success". I can't think of a better way to start a chapter. Each indicator provides an idea of what we should be looking for from our students when it comes to reading in mathematics. It then dives head first into what current research is saying about Reading in Mathematics. Some great takeaways from this section were as follows:
- reading in mathematics is a vastly different process than the reading we have our students do in other subjects.
- often the text can include elements that students have never encountered before.
- math text often contains more concepts per paragraph than other text
- math text is often organized in a manner that works against the traditional left to right reading we teach.
- mathematical text does not often repeat information
- when images are provided, they often only contain mathematical information
- reading in math requires an inner conversation that students may not by able to have without proper modeling
Within the "Reading Word Problems" section, some other great points are raised. For example, it states that unlike traditional reading, mathematical paragraphs typically place the main idea at the end of the text and in the form of a question. One recommendation that Krpan makes that pushed my thinking was the idea of providing students with the answer first. It is her belief that this could lessen the growing anxiety we are seeing in classrooms and can in turn place a higher emphasis on the development of strategy/strategies needed to arrive at the same solution.
This chapter really opened my eyes to just how different reading in mathematics is when we compare it to the "regular" reading we have students do. I feel a little more confident that we now have a starting point for how to go about addressing this issue for our students. I am excited to begin this process and really hope to share our process (successes and failures) in future blog posts.
