In 2015, The Literacy and Numeracy Secretariat released a document Making Space for Students to Think Mathematically that highlights the use of rich tasks in the math classroom. According to the document:
In choosing rich mathematical tasks, consider the following:
- Rich tasks provide multiple entry points and accommodate a variety of approaches; they can open spaces for students to participate and share their thinking, so that all students can engage with the problem
- Tasks that have high cognitive demand and multiple ways of solving problems provide opportunities for students’ mathematical thinking and discussion and, thus, challenge students to develop their understandings.
- Scaffolding students’ exploration of a rich task too early can take away students’ opportunities to explore and build confidence with solving problems in their own way
- Affording students the opportunity to explore mathematics without the pressure of imposed steps and procedures or rules can elicit a stronger response, greater engagement, and most importantly, enhanced mathematical understandings.
Consider the following traditional task on Prime and Composite Numbers. After a brief lesson, students take the table and highlight all of the numbers that are prime in yellow and composite in pink. This can be taught a variety of ways ie. all numbers divisible by 2 (except 2) are composite. By the end the students have a worksheet colour coded possibly with some errors making it hard to understand.
Let’s rethink the task and hand the students a different worksheet (or better yet, project the image below to the class). Students are to analyze the image using the questioning strategy “I Notice/I Wonder”. Try this strategy yourself and look at this image. (I haved used this at many staff meetings and watched and listened as teachers and Administrators have great conversations on what the lines/numbers/colours mean.) Now consider your students and think of the possible conversations that will happen in class. The terms prime and composite numbers may or may not come up but the idea of them definitely will. You could choose to introduce those terms first or allow the students to discover
I feel I can criticize the first ask since it is a task that I have asked my students to complete. I watched as they skip counted by twos, threes, fours and then fives. They might make it to counting by sevens but usually not, as they stop when they think they have found all of the prime numbers. Student compared their lists to each other’s and talked about it. The majority of conversations were low level – some correction of each other’s errors but not really a true understanding of what they were learning.
I’m guessing that when you looked at the second image, you clicked on it and started to figure it out, maybe even understanding all of the different aspects of the image – maybe not? Show it to a colleague, and let them list their observations. Compare. How were your observations similar? Different? Compare the discussion that you had to the discussion from the original task. Now consider your students, what do you think their conversations sound like? Given time to discuss, you probably start to hear students justifying their theories on what the colours mean, the split in the number, the small numbers and so on. As the students are working through their discussions, a mini-lesson for small groups or the whole class could be had to define the terms Prime Number and Composite Number. Some students may use prior knowledge during their conversation so those terms may come up – use your professional judgement to decide if/when that mini-lesson needs to occur.
Let’s revisit the LNS document and consider the two tasks. The first task doesn’t hit any of the characteristics of a rich task. The second task hits all of the main points as it provides multiple entry points and multiple ways of solving the problem and students are allowed to explore the question without procedures or rules.
Where does technology fit in? As always, we should only use technology when it improves practice. In this case, I would suggest a screencasting app (like Explain Everything) where students could add the image, explain their thinking orally as well as “mark up” the image with the pen tool when demonstrating some form of understanding. Having students share their Explain Everything videos with the class during a digital gallery walk will allow for students to listen to various solutions and thoughts as well as to reflect back on their own learning and correct or add to their answer.
Many simple tasks that we ask our students to do can be presented in a more rich way, a way that engages our students and provides them an opportunity to build and then demonstrate their knowledge in various ways.
Student achievement through engagement and rich tasks.