"The idea that students can be intensively, productively and successfully engaged in a task and yet learn nothing as a result seems to me to be the most profound idea in all of educational psychology."
So tweeted @dylanwiliam a number of days ago referring to mathematics classrooms. And his statement has worried me since I read it.
Here are my thoughts.
Of course students can be "intensively, productively and successfully engaged" within a maths lesson, but not doing any mathematics. In this category I include what I call the 'colouring' tasks you find on many maths worksheets. Many of these do not involve the students in any mathematical thinking at all. They are not engaged in mathematics.
Of course students might not be learning what I intended them to learn, and maybe this is what this statement means. When planning I tend to think about 'learning possibilities' rather than objectives. I have in mind possible mathematical trajectories where a task may lead. This includes the constant re-framing of the task according to what I notice going on, fed by the multitude of in-the-moment decisions I make. These rely on my experience and knowledge of both the mathematics and the learners and this changes every lesson, as the learners respond to what plays out. This is how learning is built. It certainly does not involve me concluding someone has learned "nothing". What is learning "nothing"? How would I know this? How would I recognise "learning nothing"?
Learners might be involved in something and might not appearto be 'learning'; perhaps for example when they are spending time handing manipulatives. Maybe I have been working with some Y1 children on number bonds within 10 and 20. At the end of the session perhaps they are unable to answer my question "What number pairs up with 11 to equal 20?" Does this mean they have learned "nothing" during that task? Do they understand my question? What can they tell me? If they are unable to answer me verbally, maybe they can answer whilst looking at an image?
Perhaps the statement confuses performance with learning. Maybe (some? all?) my children are unable to perform the required objective, in this case, to name the complementary pairs of numbers that total 20. But they (some? all?) may well have learned, if I have crafted my lesson well, that there are a finite number of pairs and begin to see links to the pairs of numbers that equal 10. It is my job, each and every interaction, to find out what they havelearned and build from there. How might I craft my lesson so that they learn to think mathematically? In this example the children may have been building and discussing sticks of cubes, or Cuisenaire trains, to total 20. But in order for them to be "intensively, productively and successfully engaged" in mathematical thinking, I will ask them to:
• find ways to check there are always 20,
• how they are sure they have found all the pairs,
• organise the pairs and look for (and explain) a pattern they notice,
• write the horizontal number sentence to match each pair,
• play "Which number is missing?" as they take it in turns to hide their eyes and remove one stick. We'll ask each other "And how do I know?"
But this is a suite of lessons (or sessions). In order for them to be "intensively, productively and successfully engaged" in mathematics, the practical task is one part. And may last a while. Maybe longer than 'one lesson'. So is it correct to assume that these students were, at any point"...intensively, productively and successfully engaged in a task and yet learn(ing) nothing as a result"?If I view this as one small episode in a series of planned interactions where my students and I 'meet' the pairs of numbers that equal 20 in many different ways (coins, bead-strings, patterns...) and link this to other mathematical knowledge, we have plenty of opportunities to re-visit this to ensure they have learned this particular 'something'. Learning takes place over time, not necessarily within a lesson (to paraphrase Pete Griffin) and the drive to make sure that every student is learning something every lesson (or every interaction) might lead me to conclude that "students can be intensively, productively and successfully engaged in a task and yet learn nothing as a result."
My conjecture, after thinking about this statement, is that it is not possible to be intensively, productively and successfully engaged in themathematicsof a task and learn "nothing". And that is my job as a teacher, to intensively, productively and successfully engage learnersin mathematics. My teacher-questions and interactions should focus the students on the mathematics; encouraging explaining, describing, reasoning, predicting and link-making. Tasks that do not include this, whether or not they are deemed to be 'discovery' or 'practical' or 'practice' or or 'direct instruction' are not mathematics tasks. Even when they take place in a maths lesson.
I am not sure the idea that Dylan William refers to in this tweet is profound. It is either blindingly obvious or lacks nuance in considering learning. More worryingly, it might be used to denigrate ways of working in mathematics lessons that include exploration, inquiry, discussion and handling manipulatives; and that seeks to promote direct instruction by an adult as the only effective way to teach and learn mathematics. And that is what worried me.
