Since my beginning year of teaching, my science program has focused on having students think and act like scientists. Often, the year has begun with discussions and research about: What do scientists do? What types of characteristics do scientists possess? What processes do scientists follow in order to arrive at strong conclusions? Scientific skills and concepts are reinforced throughout the year, especially during student-led projects, such as science fair.
But then I began to wonder, what about math? Why haven’t I focused on having students think and act like mathematicians? Don’t mathematicians possess many of the same characteristics and perform many of the same skills as scientists? How can I plan the curricula to have students think and act like mathematicians?
I have always grappled with providing a balance between teaching specific concepts and outcomes, and essential process skills, such as problem solving and communication of ideas. My previous years of teaching math had focused more on teaching the basic skills, rather than creative thinking and process skills. With the increased accessibility of every type of information, I have found it increasingly important to teach process skills, such as accessing and using this information.
My plan to have students think and act like mathematicians is still being formed and will be forever ongoing. This action plan has been taking shape through collaboration with my curriculum partner, Carolyn Armstrong, conversations with my students and simply finding the ‘teachable’ moments within topics. Through conversations with students, we decided that mathematicians are very similar to scientists (perhaps because they are), and possess many of the same qualities.
Students have said that mathematicians:
• “Should be able to use different strategies effectively when doing a difficult problem.”
• “They have to look at problems from different angles, allowing all possibilities into play.”
• “Communicate ideas with peers and teammates to help conquer a problem or question as an efficient group.”
• “Help improve Science and the quality of our daily lives.”
• “Have very good problem solving skills, they let the math speak for itself.”
Through discussions and problem solving, my classes have decided that mathematicians:
• solve problems,
• make conjectures (this idea was learned through a specific problem),
• work within a community of others,
• share their work and ideas clearly,
• document all their thoughts (even mistakes),
• are persistent and try many ways to make something work, and
• are creative thinkers (some students are still not convinced by this point).
A few activities that we have undertaken to think and act like mathematicians include:
• Problem solving: Students are encouraged to find their own ways to solve problems, while working within conversational groups. It is essential to provide students with deep problems that allow them to explore concepts and discuss ideas.
• Group work: Having a community of learners, all focused on the same goal, is key to solving more difficult problems. We have practiced many group work skills, such as equally sharing work and taking roles, in order to become more comfortable with creating and sharing ideas collaboratively. Often, individual thinking time is allowed, before beginning group work.
• Communicating ideas: This includes both verbal and written communication of ideas. Students have been specifically taught how to write-up their problem solving process, letting the math speak for itself. This is an ongoing lesson, which is constantly reinforced in class. Verbal communication is practiced in group work and class debates/discussions.
• Letting math speak for itself: We have made a distinction between math and language arts, as many students preferred to write paragraphs describing their problem solving processes. Through modeling, students have become more adept at providing proof using mathematical equations and statements.
• Following the natural progression of concepts: In previous years, I had a very regimented plan of which concepts to teach in a specific order. This year, problems designed for a specific purpose/concept have often led to teaching concepts I had not planned on. Instead of ignoring this, I have tried to find the ‘teachable’ moments and ‘go with the flow’. For example, a question about rounding and significant differences resulted in a review of percentage. Teaching concepts in context provides real opportunities to practice.
These activities and goals are constantly modeled and reinforced with a variety of topics. Students are beginning to see the value in thinking and acting like mathematicians. When asked “What are the most important skills you’ve learned in math class this year?”, most students identify process skills, rather than specific math concepts:
• “I think the most important skill I have practiced the most and will benefit from is finding the best possible strategy to use when solving the problem.”
• “Knowing how to approach a problem, knowing the proper procedure, and thinking it out logically.”
• “Probably how to write up a problem because I am starting to get more neat and don’t lose track of what math I did earlier on the same problem.”