Dan Siebert recently had a paper titled “Students’ Structural Reasoning About Rational Expressions” published in the conference proceedings for the Psychology of Mathematics Education – North America conference. Dan has answered a few questions about this paper below:
Who were your co-authors on this paper?
Dana Steinhorst, a former graduate student
Who would you say is the target audience for this paper?
Mathematics education researchers
What is the big problem you hoped to address with this paper?
We wanted to understand what structures students perceived and reasoned about as they simplified or solved equations involving rational expressions.
What are some of the key ideas in the article?
Past research indicates that students seldom attend to structure as they simplify algebraic expressions or solve equations. However, this finding is largely due to researchers only collecting students solutions without asking them about their reasoning. While students in our study did not always identify and reason with correct mathematical structures, they nonetheless consistently identified and used mathematical structures in all parts of their solutions. Correct solutions were characterized by using structures that honored the order of operations, matching those structures to correct rules and properties, and evaluating matches to see if the application of the rule produced progress toward a solution.
What are some of the main ideas you hope your audience will take from the article?
Students naturally look for structure in algebraic expressions and equations, but do not always identify helpful structures. They need instruction that teaches them to use the order of operations to identify correct mathematical structures and substructures, to match those structures to appropriate rules, and to evaluate the progress made by applying the rules