The strategies we use to teach math are coming under a lot of consideration these days.
I do believe that curriculum frameworks are changing for the better within a changing society. We are moving from a purely behaviouralistic view of curriculum as drill, repetition, basic skills instruction and review. Curriculum under this view is highly prescriptive by nature, and requires step-by-step structured learning methods. However, I think that it is problematic to spend our time here for many reasons – one particular reason is because the answer to anything can be googled.
It is important to focus on the language of math and our subjective realities that come into play when we are working with mathematical language.
Communication is therefore the cornerstone of math. Math makes use of symbols that we have given meaning to. Therefore, adding dimensions and new realities with communication is essential to creating a full understanding of the symbols and what they mean to others – and what they mean to us.
Constructivist views are concerned with thinking about how students learn – I agree that it is important to actively involve the student in the process of thinking and learning about math.
I also appreciate that we are moving toward phenomenological perspectives with our curriculum and finally starting to view individuals in relation to the work they are doing. It is important to get at the desires, feelings and understandings of our students – this is at the heart of self-esteem and is essential to learning.
Students must feel confident, eager to learn and have their work be satisfying. Don’t we all need this??
I think that math and problem solving also needs to account for, and incorporate individual creativity and student inquiry to these ends. Communication is essential for this to happen.
You may have different theories about math curriculum however, and we all need to come to our own theories.
Math Mindsets and Communication
At this day in age, I am always surprised at how many mindsets about math still involve beliefs about drill worksheets and working out of a textbook. We are recognizing that how we communicate about math affects our mindsets. Positive math mindsets can boost student achievement in math.
Communication is just as important in math as it is in other subject areas. It is simply never enough to do basic drill and kill practice of multiplication facts. My philosophy is that the math facts need to be embedded within tasks and contexts that require creativity, problem solving and communication. I like to embed this within a ‘Gradual release of responsibility’ framework.
Gradual Release of Responsibility
The way I work with math literacy is actually very similar to how I work with language literacy in my classroom, and I keep in mind the gradual release model of responsibility for all students. I always start my lessons with the whole group. This is the opportunity to introduce the task, goals, vocabulary in addition to engaging in diagnostic assessment. This helps me to further determine how I will further adapt my instruction to meet the diverse needs of my students.
Talking circles is just one strategy that I use in my whole group instruction to create shared understandings and determine how students are thinking about the math. I am able to promote growth mindsets and a safe environment to have my students share and justify their strategies and ideas about our past learning, in addition to asking further questions and clarifying the answers of others, and set new goals. This is our opportunity to learn from each other in addition to honing in our own mathematical understanding.
We then may move toward a shared activity, this could either be as a whole class, but with me, more often than not, the students work in groups on key mathematical problems that build their knowledge and skills together. I am facilitating the learning by allowing students to get ‘stuck’, ask each other questions, try out multiple strategies based on what we have already talked about or done as a whole class. I am also there to help scribe, provide cues, more visuals, and any other strategies as in IEPs or as needed.
Sometimes, I work with guided groups. Here, I ask students to summarize for me, focus their attention on the key terms, concepts and strategies. I can be explicit again with what exactly they are learning and why, provide more examples and present material in sequenced steps if needed. I can also check for understanding and ensure that the students are understanding tasks and directions.
It is after this work, that I like to have groups present their strategies, using accountable talk, key knowledge and understanding. Sometimes we post up our work around the room after our presentations.
After this, the students engage in a gallery walk around the room with post-it notes – their task is to provide at least 2 questions to other groups about their strategies (lessons in asking strong questions occur in our class too:). After this, the groups go back up to their work and answer the questions for the class.
It is now, that students have had lots of modelling, and a gradual release of responsibility with the concepts, that they can now move to their own individual work to demonstrate how they, or if they have been able to consolidate their learning. Those who are still not ready, sit at the back of the room with me in guided math groups, with further accommodations and modifications to ensure success.
I believe that effective communication is the backbone of math success. These are just strategies that naturally work for me.
What communication strategies work for you?
Ministry of Education: Capacity Building Series:
Youcubed by Jo Boaler: