This post is one I have been meaning to write for a while, at least 2 years in fact, I have wanted to share it as it has had a dramatic impact on my own classes and also on that of other classes in my school, I guess I just never have gotten around to writing it down. Teachers at our school have made the decision to not to use textbooks to teach mathematics in the middle school. I think that this move has been a very positive one for our school. It is not that I feel that textbooks are evil, in fact I feel their quality has improved in recent years. However I feel there are still some parts of their design that impact on how people with engage with them, staff and students alike. When making the decision to no longer use a textbook for maths class I needed to find an appropriate replacement. Textbooks are good at providing lots of questions for students to practice the skills they have learnt, and this practice is important. However I needed to find an option that did not have the excessive scaffolding and the extensive quantity of questions that I saw in most textbooks. Many of the worksheets I found online has the same characteristics at the text books, so I began to think about how I would design problem sets myself. Designing the problem setsWhen I sat down to think about how I would design my problem sets I wanted to keep some design criteria in mind these criteria were:
One of the question sets I came up with are shown below. Underneath that image I will explain the design of them.
Impact of the problem setsGreater levels of metacognition One of the most interesting observations I have seen from students engaging with these problem sets is that they seemed to become much more metacognitive. This is evident in where they choose to start with the question sets. Some have talked about believing they can do the level 2 questions, but really want to work on a few level 1 questions first to make sure they have it. Others have attempted the level 2 or three questions, given it a go for a while, haven't made progress and have moved back to try the level 1 questions. There have also been students who have looked at the level 1 and 2 questions and have made the determination that they know how to do them and have spent their time only working on the level 3 questions. This process of having three different levels of question to choose from has made them much more aware of themselves as learners and of what they need to do to move their learning forward. All students have had the time they have needed to work on their questions of choice In looking at the problem sets with my class now, I feel that they all feel as if they have enough time to work on the questions they have chosen and feel comfortable attacking. If I take the level 1 questions for example, I know that some could be through those questions very quickly and there are some that will take much longer. If I look at my classroom about 5 years ago I would say that the time I gave them to do the questions was aimed at the the middle, the ones who had it finished early and got bored and the ones who were struggling never had enough time to finish them. With students working on different difficulties of questions they all seem now to have the time they need to finish the questions. They are attempting much more challenging work The comment I get a lot when students are working on these problem sets is "why do you have to make it so hard". This is normally from students who are working on the level 3 questions. My response in this situation is always the same "Doing the level 3 questions is your choice not mine, so you are making it hard on yourself" to which they normally reply something along the lines of "yeah well those other ones are too easy". What is clear through this is that they they are no longer just happy to do the easy ones, the could do that and finish really quickly, but they don't. Students seem to be really working on questions that they feel are just beyond their current level of understanding and they are striving to understand them. I can now see the slow, deep mathematical thinkers Having done the Jo Boaler courses one point that is emphasised a lot is not to make maths about speed. It talks at length about how mathematicians do maths, how they are deep slow thinkers. Reflecting on previous practice I realised that for those deep slow mathematical thinkers, there was a time that my classes did not offer anything to those students, I didn't even know they were there. I didn't see them because their diagnostic data backed up what I saw in class, but that was because I was asking them to work in class in similar ways to which the test was administered. What I am seeing now is that there are quite a number of students who do not perform well under the time and pressure of diagnostic testing, but have flourished with these problem sets as they have the time to sit with the problem and think about it rather than being pushed through endless problems. They are showing much greater levels of mathematical thinking than some others who score much more highly on those high stakes tests. The quality of their work is much better I have seen a noticable improvement in the quality of the work I recieve since using these problem sets. Much of it I think can be attributed to giving them problem types that allow them to demonstrate their understanding and then the time to work on them. What I find challenging about these problem setsDespite the massive, dramatic change these problem sets have made to my class, I still struggle with some aspects of them. Most of these are still the tug of war I have inside myself about getting the balance of mathematics right in my classroom
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Senior Leader of Pedagogical Innovation and Mathematics Coordinator in Regional South Australia.
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