How To Learn Math #4

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Recently, I began a MOOC (massive open online course) called How to Learn Math – For Teachers and Parents (2).  More than 40,000 people took the last class – mainly teachers, parents and school administrators. 95% of people completing the end of course survey said that they would change their teaching or ways of helping as a result of the course.  The course offers important new research ideas on learning, the brain, and math that can transform students’ experiences with math and is based on the work of and narrated by Jo Boaler.  It’s divided into 8 sessions and each one ends with a prompt to write a one paragraph summary reflection on the ideas.  My plan is to post those reflections here.

The fourth session is titled, Teaching for a Growth Mindset.  The focus of this module is on the various strategies that teachers and parents can use to promote a growth mindset in mathematics.  There are 3 ideas that spoke to me here.

Grouping strategies can result in lower achievement.  We call it tracking and the research that Jo Boaler points to concludes that tracking within and throughout classes sends fixed mindset messages to students especially the high achievers.  Furthermore, tracking tends to confine students to a lower track when tracked early on.  In countries like Finland and Japan, who track the least and latest, students tend to show more success.

When students are tracked there tends to be different teacher expectations applied to different ability groups, even when teachers try not to or don’t want to have different expectations.  Students in lower groups are generally given easier work which limits their achievement.  Teachers tend to teach to the middle of the tracked group assuming everybody is the same so everybody gets the same work at the same pace.  So there tends to be little differentiation in tasks assigned and in instruction.  Even in a tracked group, there tends to be a range of ability because often some are misplaced.

In untracked groups, teachers are more likely to recognize that there is a range of ability and that they need to provide differentiated opportunities.  These opportunities include giving more “open-work” that students can take to any level and differentiating the instruction for students.  When the environment is structured properly, untracked students are more likely to choose higher level work, they achieve more, students choose more advanced courses, and students are more likely to pass national tests.  These results occur across the achievement range.

The kinds of tasks we ask students to work on can negatively affect their mindset.  If they’re short, enclosed, with one right answer, students are either getting them right or wrong.  Under these conditions, it’s really hard to develop the idea that mathematics is about growth and learning.  If a student is constantly getting the wrong answer, it can be really hard to believe that they can do math.  So tasks need to give students the space inside them to learn and to see that math means learning, not just performing.  Teachers need to design tasks so that students can see them in different ways and can start it from where they’re at by choosing a strategy that suits them.  There should also be clear learning goals and adequate opportunities for feedback.  In many cases, teachers only need to modify tasks that they already use.

Summative assessment should probably be eliminated.  It tells students how well they’re doing compared to other students but it doesn’t tell students about their path to growth and improvement.  Effective assessment should tell students where they are, where they need to be, and how to close the gap between the two.  I know this as formative assessment.  Studies have shown that among students given only summative assessment, only formative assessment, and a mixture of both, the students given only formative, achieved significantly higher than either of the other two.

In order for formative assessment to be effective, there needs to be a level of awareness on the students’ part especially for knowing where they need to be.  So starting with learning goals becomes so important and using those learning goals to self and peer assess helps to build that awareness.  In another study, two groups of physics students were given equal time to work together on the subject matter.  One group simply discussed the work while the other self and peer assessed.  The latter outperformed the former on three different assessments and the greatest gains were made by those who were previously low achieving.  The research suggests that low achievers are often low achieving, not because they lack ability or because they’re slow, but because they just don’t know what’s important or what they’re meant to be paying attention to.

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