I have had the privilege of hearing Christine Suurtaam (Associate Professor. Faculty of Education, University of Ottawa, author and presenter) speak a few times. She speaks on a wide range of topics, from her work with patterning and algebra, to her research around the Grade 9 Applied Math project, to supporting students in fostering mathematical thinking. She co-authored a ministry monograph "Making Space for Students to Think Mathematically". It highlights the importance of supporting mathematical understanding for all students.
Here are the "Coles Notes".
We can support student understanding by:
- providing a safe space for taking mathematical risks
- allowing for exploration and collaborative learning
- presenting rich tasks and encouraging high-quality student interaction
- creating a math talk learning community
- asking good questions and listening to student thinking
In establishing this type of environment for our students, we support questioning and explanations and consolidate student thinking and understanding. During this process, students are able to compare and connect their ideas and strategies with other students. This provides opportunities for further questioning.
Selecting rich math tasks allows for a range of learners to participate in the learning and provide an element of exploration. This, in turn, generates discussion and thinking in varied ways. Chris Suurtaam offers a cool math task that focuses on proportional reasoning:
Tug of war 1: 4 frogs on one side had a tie with 5 fairy
godmothers on the other side.
Tug of war 2: 1 dragon had a tie with 2 fairy godmothers
and 1 frog.
Tug of war 3: 1 dragon and 3 fairy godmothers on one
side and 4 frogs on the other side.
Who would win the 3rd tug of war?
This type of math task not only provides "a way in" for students with a range of abilities, but it also encourages students to use manipulatives, draw, collaborate, act out, etc. in order to solve the problem. The consolidation of thinking that would follow would be critical to student understanding. This would be facilitated by the teacher through good questioning and "interpretive listening".
If you get a chance to look at the monograph, it's worth the read!!
I read your post then followed and read the link to the ministry monograph and found it quite interesting.
ReplyDeleteCritical thinking is arguably one of the most important skills students need to develop. It’s not something that students will just naturally get good at on their own, either. It needs to be developed over time and with help. Too often we ask students to think critically about something, but don’t give them the tools to do it. When they fall short, teachers tend to just give the answers and move on with the lesson.
The research monograph you’ve shared with us helps explain how to actually develop critical thinking abilities. What’s more, it gives sample questions, sample conversations, and how it’s been used in the classroom. I already strike up conversations with students as I circulate, asking simple knowledge questions to higher thinking questions, but I never thought of a “math talk community”. It is certainly something I’m going to look further into.
Thank you for sharing!
I completely agree that Critical Thinking is so important, especially in a math class setting. Critical thinking is a skill that can so easily transferred into a real life situation, and it’s so important that students learn the skills needed in school to be able to critically think.
ReplyDeleteAs Vanessa pointed out in her comment, there are so many times that teachers ask students to critically think about a subject, however we often rush the students through this process. There is a really good line in this article (https://tc2.ca/uploads/PDFs/TIpsForTeachers/CT_elementary_math.pdf) that I particularly enjoy: “Time invested in developing critical thinking pays off when students “learn to think and think to learn.”” As mentioned above, critical thinking is so important in everyday life as well. When we teach students to think critically, we are developing so many more skills than just those that are related to the maths. Another article (http://www.criticalthinking.org/data/pages/8/6e11be66504d96cebb64d251d6ece5ba519e87f8a7c60.pdf) that I enjoy is this one that contains teachers’ opinions on Critical Thinking, what their definition is, why they think it’s important, and/or how they implement it into their classrooms.
I also found that the Research Monograph that you posted here contained some very good ideas. Does anybody else have any in class strategies or suggestions that could help me build my repertoire?
I completely agree that Critical Thinking is so important, especially in a math class setting. Critical thinking is a skill that can so easily transferred into a real life situation, and it’s so important that students learn the skills needed in school to be able to critically think.
ReplyDeleteAs Vanessa pointed out in her comment, there are so many times that teachers ask students to critically think about a subject, however we often rush the students through this process. There is a really good line in this article (https://tc2.ca/uploads/PDFs/TIpsForTeachers/CT_elementary_math.pdf) that I particularly enjoy: “Time invested in developing critical thinking pays off when students “learn to think and think to learn.”” As mentioned above, critical thinking is so important in everyday life as well. When we teach students to think critically, we are developing so many more skills than just those that are related to the maths. Another article (http://www.criticalthinking.org/data/pages/8/6e11be66504d96cebb64d251d6ece5ba519e87f8a7c60.pdf) that I enjoy is this one that contains teachers’ opinions on Critical Thinking, what their definition is, why they think it’s important, and/or how they implement it into their classrooms.
I also found that the Research Monograph that you posted here contained some very good ideas. Does anybody else have any in class strategies or suggestions that could help me build my repertoire?
I think the idea of students feeling comfortable to take math risks, explore and not be afraid to get wrong answers is very important. I agree with the significance of critical thinking and think this also ties in closely with the process of reflecting. I think an important aspect of reflection that can extend to any subject is to encourage students to question the validity of information presented or look for other methods of expressing an idea or alternate solutions and then draw conclusions. This helps students obtain a better understanding of concepts and promotes a deep understanding versus a more superficial one. An example I’ve used with grade 8 math was to challenge the students to come up with different approaches and methods to approximate the area of a circle using a variety of tools and materials. They would then reflect on these different approaches to develop formulas to approximate the area and consider which approaches allowed the best approximations and were closest to the actual formula. I was always surprised and impressed by some of the ideas and lateral thinking that students came up with.
ReplyDelete