Mathematical Disposition and Student Beliefs: Part 3: Whole Group and Guided Math
Beliefs are Big. Students beliefs about math and themselves as mathematicians “exert[s] a powerful influence” on what students think they can do, they are capable of doing, on how much they will try, how much they will stay engaged with the math and ultimately on their mathematical disposition. (NCTM, 1989, p. 233).
Because we know that there is a definite relationship between what students believe and teaching and learning, we have to think about how we as teachers take this into account when teaching math. By third grade, students have these really ingrained beliefs about themselves as learners in all curriculum areas because they have had ample experiences. So, they either believe that they are really good at something or that they suck!
Given these mathematical autobiographies, what do we do? How do we shape or in many cases un/shape their mathematical dispositions? How do we help shift students’ negative belief systems about math and themselves as learners?
Spangler (2000) did a study where she asked a series of interesting questions, in order to unearth some beliefs and engage in a deep discussion about math springboarding from the answers. Ask your students these questions, and compare their responses with the ones from the study. Think about how to use these to spark discussions about math. Here are some of the questions.
If you and a friend got different answers to the same problem, what would you do?
Spangler found that most of the students said they’d check to see who was right and often times they would default to the student who was believed to be more capable. She points out that this highlights a common belief that math is about getting the one right answer. This conversation can lead the students into thinking about how there can be more than one right way and one right answer in math.
If you were playing “Password” and you wanted a friend to guess the word “mathematics,” what clues would you
give? (“Password” clues must be one word and may not contain any part of the word “mathematics.”)
Spangler found that the most common responses were add, subtract, multiply and divide. She points out that this highlights a common belief that math is about computation. This conversation can lead into a discussion about how math is so much more than arithmetic.
How do you know when you have correctly solved a mathematical problem?
Spangler found that students said they would recheck their work to make sure there were no errors. She points out that few students thought about if their answer made sense. Students failed to think about the context as a way to reason about their answer. This answer leads directly into a discussion about thinking about the problem solving situation and the answer in a given context.
Close your eyes and try to picture a mathematician at work. Where is the mathematician? What is the mathematician
doing? What objects or instruments is the mathematician using? Open your eyes and draw a picture of what you imagined.
Spangler suggests, “Ask students a variety of questions about the mathematician they imagined. Was their mathematician male or female? How old was their mathematician? What was their mathematician wearing? What did their mathematician look like? In what types of activities was the mathematician engaged? Were there other people around?
Spangler found the results very similar to the ones when this same question is asked about science. She noted that
“In the case of the mathematician, the students generally picture an older male with grey Einstein-like hair, wearing glasses, and sitting at a desk. He is usually using pencil and paper, books, a calculator or computer, and sometimes a ruler. The mathematician is often in a nondescript room, and there are no other people around.”
One way to get them to see math as a real world endeavor is to talk about the following questions.
Do you suppose McDonald’s has a mathematician on its corporate staff? What might that person do for McDonald’s?
Spangler found that the students said things like count how many people came or how much money was made. She writes that “To stimulate additional thought, the teacher can pose some real-world questions: How does McDonald’s decide where to build a new restaurant? How does McDonald’s decide on new food products to offer? How are the promotional games created? These questions open the doors for discussions about data collection, statistics, and probability.”
Questions I might add:
Do you think Disneyland hires mathematicians? What do you think they do for Disneyland?
Do you think ABC, NBC and CBS hire mathematicians? What do they do?
Do you think that the secretary, the custodian and the cafeteria director use math daily? How?
How do you use math daily?
These types of questions are a great way to spark conversations and unpack beliefs about math. Try them and let me know what you find out.