Tag Archives: math curriculum design

Sticky Learning

I recently gave a TEDx talk about this topic but for those of you who like to read….

Tradition and intuition play a big role in how we teach but our observations of student learning and research suggest that we might be wrong.  Traditionally we teach in units:  2, 4, or 6 weeks (albeit they sometimes stretch into 8 or even 10 weeks).  We think that if we teach the kids all they need to know about one subject (multiplication, persuasive writing, levers, time, the colour wheel etc) and give them lots of practice about this one topic, over and over again in a 2-4 week period of time, then they will learn the stuff.  Except, they don’t.  Students don’t tend to retain concepts they only learn once a year very well.

Our observations of student learning show us that this is true.  If you teach fractions, usually taught in a 4-6 week unit in the spring, you know this.  It feels like every year is like starting over.  I’m sure that you can think of many other concepts where the learning done last year doesn’t “stick”.

There is cognitive research that does tell us a lot about how people learn.  Two concepts, spaced learning and interleaving, are well-documented in the research but hold little traction in real classrooms.

We typically teach in a “massed” practice where we teach kids everything about one topic in a short period of time and then test them.  Students do well in testing situations immediately following the learning, but test them a few weeks later and they don’t remember very much.  However, when material is learned spaced over time, retention of concepts is much greater.  This positive effect has been documented in the literature since 1885!  John Hattie, in Visible Learning, listed it as the 13th most positive effect on learning out of 138 possibilities.  You may wish to consider what would happen if you took a big topic, like fractions or division or proportional reasoning, and instead of teaching it all at once, you spaced the learning out over multiple  opportunities over the course of the year.

We have found spacing the learning out to be very beneficial to our students.  For example, instead of our intermediate students reading just one novel over 6-8 weeks (and really, as a real reader, who does that except maybe for War and Peace?) our students read between 6 to 10 novels over the course of the year, spending between 2-3 weeks on each.  They learn all the same skills about analyzing literature, but they have multiple opportunities to practice the skills over the year.  We do the same in mathematics, returning to problems in proportional reasoning, for example, a few times every month instead of in a 3 week unit.

The other piece of research that has huge benefits for learning, but doesn’t really hold much traction in our school system, is interleaving.  We tend to block the curriculum into discrete units of study, studying each topic one at a time:  addition, subtraction, multiplication, division ; OR, fractions, decimals, percent; OR, persuasive writing, descriptive writing, report writing.  The problem, when students learn this way, is that they don’t learn to see the similarities and differences between the topics.  We hope they will make connections, but really it is left up to them to do it on their own.  When we teach like this it is called “blocked practice”.

But if you interleave the learning, you teach similar concepts all at the same time.  A writer’s workshop model allows students to explore a variety of forms of writing all within the context of writer’s craft.  If students were faced with problems in mathematics involving addition, subtraction, multiplication and division at the same time then they would be forced to develop an understanding of how the concepts are related and to know when to apply each concept.

I call teaching in this spaced and interleaved way spiralling.  While provincial and state curriculum  say they “spiral”, meaning that students learn about fractions, for example, once every year, I argue that the spiral loops are too big.  If we tighten the spiral so that students have many chances to learn the big ideas over the course of the year, I think we get to learning that is sticky.

Of course, spiralling is not easy to plan for.  Teachers like their units.  They like to be “done”.  Spiralling the curriculum really requires that teachers adopt a new mindset about curriculum design.  It isn’t easy…but the teachers that I work with wouldn’t ever go back to teaching traditionally in longer units.  Not only do we get sticky learning, but our students are much more engaged.  Every day is a new challenge for them and they have to apply their learning to specific and varied contexts.

If you want to give it a try, think about doing just a bit at a time instead of revamping your entire curriculum.  Try something new; no one will die.






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