“I wish I’d known that when I was teaching" is something I said to myself several times while I was working on the latest Insights for Teachers report. The National Monitoring Study of Student Achievement (NMSSA) released the Mathematics and Statistics Insights for Teachers report this month. The report is designed to support the teaching of mathematics and statistics in primary and intermediate classrooms. It draws on insights from hands-on mathematics assessments completed by students in 2018.
I was lucky enough to have been involved in the development of some of the tasks that were used for student assessment. It was great to be able to delve deeply into topics such as spatial reasoning and collaborative problem solving. The report shares some of our discoveries with teachers, both from the NMSSA study results, and from the research.
The Insights for Teachers report focuses on three areas of mathematics and statistics – spatial reasoning, fractions and percentages, and collaborative problem solving. While I contributed to all three sections, my main area of interest has been in the area of spatial reasoning. Defining spatial reasoning can be challenging, but it generally includes two facets – mental rotation and spatial orientation. I find it easier to think of mental rotation as the skill you use when you picture what a room would look like if you moved some of the furniture around, while spatial orientation is the skill you use when reading and following a map. When someone parallel parks a car or plays Tetris, they are using spatial reasoning.
What was most interesting to me was finding out that early ability in spatial reasoning is a strong predictor of later success in STEM (Science, Technology, Engineering, and Mathematics) disciplines. People who work in these fields often use models, maps or diagrams to solve problems, so the skill of being able to visualise 2- or 3-dimensional objects in the mind is vitally important. It is said that the renowned inventor Nikola Tesla was able to visualise and manipulate whole structures in his mind before committing them to paper!
One of the tasks we gave the students was called “Building in the Mind’s Eye”. Students listened to some step-by-step instructions on how to construct a 3-dimensional model using plastic cubes. They were then shown photographs of four models and asked which one looked like the picture they had built “in their mind’s eye”. This task became challenging when there were more transformations (e.g., turning, flipping) included in the instructions. This task could be easily replicated in class and will help students develop these important visualisation skills. The Insights report includes the instructions we used with the students as well as details on another spatial reasoning task, “Moving Models”.
The report explored two other focus areas – Fractions and Percentages, and Collaborative Problem Solving. The Fractions and Percentages section unpacked three tasks which highlight some of the challenges involved in teaching this area of the curriculum, such as the importance of proportional relationships. In the Collaborative Problem Solving section we gave pairs of students a problem to solve together. It was pleasing to find out that most students could work together on this problem, even if they had been randomly selected as partners. The report goes into more depth about the variation in methods and thinking used by the students to solve the problem.
At the end of each section in the report is a list of things that teachers can do in their classrooms to enhance learning in that focus area. For instance, giving students opportunities to do puzzles, play with blocks and tangrams, and complete mazes are all excellent ways to develop spatial reasoning. There are some great board games available that also assist in developing these spatial skills. Considerations when teaching fractions and percentages or embarking on collaborative problem solving are also provided.
As I was writing this report, I found things I wish I’d known when I was teaching. I hope teachers reading it now will find the information as useful and interesting as I did.
NMSSA assesses student achievement across the New Zealand Curriculum (NZC). Each year it assesses Year 4 and Year 8 students in one or more learning areas using nationally representative samples. In 2018 Social Studies and Mathematics and Statistics were assessed through a series of paper-and-pencil and hands-on tasks. Insights for Teachers reports are currently available in Science, Health & PE, Social Studies and Mathematics and Statistics. These reports are available on the NMSSA website.
Teresa Maguire is a Researcher/Resource Developer an NZCER
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