(In the same week that I wrote this, Carl Oliver posted on a similar experience. I recommend that you go and read ‘CLOG: They chose the worksheet?!?!‘ for some interesting reflections.)
I like to give my university students choice about the kinds of questions they tackle in tutorials. Usually it’s as unsophisticated as grouping questions by type and giving them the choice of which ones and how many they tackle. Sometimes I add more open questions (for example, like those in Marian Small’s ‘Good Ways to Differentiate Mathematics‘). Quite frequently I include hands-on activities, for example, cut-and-match card sorting tasks like those that result in the solutions shown below.
Tasks like these are fairly atypical of university maths tutorials. Because they are out of some students’ comfort zone, I also make reference to textbook questions that are similar in learning objective. (I recognise though that there is a big difference between asking students to graph a quadratic ‘from scratch’ and to match different representations of the same quadratic.) My own preference is for these tasks that encourage students to talk with one another — to explain and justify their reasoning, to make connections, and to construct their own strategies for translating between representations.
Last week I noticed that roughly half the class jumped straight into the card-matching task, and half the class started on textbook questions of some type (but may have switched to the card-matching task later). Of those that I saw on the hands-on task, roughly half used scissors to cut out and rearrange the cards, and half annotated the handout.
I wondered about their choices, so I thought I’d ask them to tell me more. I quickly devised two questions and asked them to respond on a scrap of paper. Here is a selection of the responses I received (the number of responses for ‘textbook’ or ‘card’ won’t match with what I observed earlier).
1. Do you prefer card-sort activities or ‘textbook’ questions? Why?
2. When you do card-sort activities, do you prefer to cut and rearrange, or do them on the sheet? Why?
- I prefer text book questions, with lots of examples, and I like when you have step by step examples. That’s how I learn best.
- Textbook because there are examples to learn from and multiple sets of questions. On sheet because it saves time for more maths and stays neater.
- Textbook questions. Easier to go back through when revising.
- Textbook questions because there are lots and you can check answers immediately. On the sheet because it’s less messy.
- Cut out exercises better because you can work out by moving them around and leave the difficult till last. Cutting out and seeing a visual representation is better than just numbering for me.
- Mixture of both, card sort keeps it different and not dry. Rearrange as if you make a mistake you can see it easier.
- Card sort are more enjoyable. On sheet is less hassle.
- 1. Card activities. But textbook is easier when alone compared to card activities. 2. Cut and rearrange. Can easily rearrange mistakes whereas writing required rubbing out.
- Card questions because they have more variety. Do them on the sheet because cutting takes ages.
- I prefer cut out activities, they are more engaging and easier to understand how to visualise. I like them on the sheet. It is easier to keep for reference when I look back at it. Cutting out is too fussy and annoying
- 1. Mix of both. Textbook questions are good for learning foundation work but card-sort implements it to make sense. 2. Rearranging, as I can see the equations match up and then ‘fits’ in my brain. It doesn’t look as confusing to me.
- 1. The activities add a more ‘hands on approach’. This is ‘unusual’ for maths which is normally seen as boring textbook work. I like how it changes the attitude -> activity, not questions. It keeps interest up and motivation as its easy to move to a different part if stuck. 2. I do both. I often start on the sheet where I can see everything, then I cut and piece together to check my work. Its a good way to go over your answers and double check (and actually pay attention to your solutions).
- I prefer the card-matching activities to the text book questions. This is because it is easier to work out problems when you can move answers around. You can also use process of elimination to determine the answer which means you can complete the task even if there is one part you don’t get.
On reflection, I wish I’d added another question asking how they think the different styles of activities influence how they learn, but that’s the drawback of on-the-spot planning! What would you want to know? What would you ask?
This is SO INTERESTING!! There are a number of things I would wish to know. I wonder how students in the textbook camp differ in math backgrounds, like if they had a lot of success in a traditional way or not. I wonder where they are in the learning of this concept. If it is something they think they really understand, so they want practice, or it’s something they really don’t understand, so they want the step-by-step and the strategy. So many questions…
Either way, I think it’s interesting that you did some on-the-spot planning that added on to some of my on-the-spot planning. I’m honored that you took time to read my post and then ask the question. Let me know if you pursue this line of thinking any further!
I agree. So many questions! So interesting! Thanks for all the ideas. Not sure if I’ll take it anywhere with this group. But there is always the next crowd … (Not sure if you remember, but we met briefly at the MTBoS booth at NCTM. Great to connect again in cyberspace.)
This one is interesting “I prefer text book questions, with lots of examples, and I like when you have step by step examples. That’s how I learn best.”
My first response was “That’s how you learn *what* best?” Step-by-step examples are great for learning things that are step-by-step, but may not be best for getting a feel for things so you can use them in unfamiliar situations.
But then I thought, well maybe that’s what they think maths *is* — a list of step-by-step things you have to remember and practice. Is there a way to help them think differently?
Or perhaps the problem is that no matter how much discussion and conceptual stuff you do, there will still come a time when you have to do a textbook/exam style question and that is a totally different skill. Perhaps that particular skill needs some modelling by a teacher and a decent amount of practice and they are just recognising that this is so.
Hi Amie, Dan from Desmos here. At Desmos we’ll be releasing a card sort authoring tool in the near future. We’d like to release it preloaded with some useful card sorts and we thought the card sort you posted here fit the bill.
Would you let us consider re-creating it in our software and releasing it when we launch? Promises:
We won’t sell your card sort.
We will release it for free use and modification by teachers.
We’ll credit you.
Let me know what you think!
Sure, but like many good teaching resources, it’s not originally mine ;).
Comes from a UK resource called ‘Improving learning in mathematics’.
I can’t immediately find it on the web but I’m sure it was free, so I can email it to you. Address?
Ah. I should have known that was one of Malcolm’s. No problem. I’m on it. Thanks for the pointer, Amie.
Excellent. That resource contains several others, too. If you find a public shareable link, I’d appreciate the tip-off.