Dan Siebert recently had a paper titled “Uses of the Equal Sign and Equation Types in Middle School Mathematics Textbooks” 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?
Who would you say is the target audience for this paper?
Math Education Researchers
What is the big problem you hoped to address with this paper?
To better understand what meanings of the equal sign are used in secondary school mathematics and how to decipher which meaning is appropriate in a particular context.
What are some of the key ideas in the article?
We found that middle school curricula use three different meanings of the equal sign: operational, relational, and assignment. We also found that which meaning was appropriate for a particular equation depended on the type of equation it was.
What are some of the main ideas you hope your audience will take from the article?
Rather than teaching students to always think of the equal sign relationally, we believe that students should learn all three meanings of the equal sign and when to use them.
Research suggests that students’ difficulties in studying algebraic topics in middle school can be remedied at least in part by teaching students to use a relational meaning for the equal sign to reason about equations. However, little empirical research has been done to investigate what meanings for the equal sign and equation types are common in middle school mathematics. This study examines two series of 7th and 8th grade mathematics textbooks to identify what equal sign meanings and equation types are being used in middle school mathematics. Three meanings for the equal sign were used in all four textbooks, and each equation type was typically associated with only one meaning of the equal sign. The results imply that students need to develop three different meanings for the equal sign to succeed in middle school mathematics, and that recognizing equation types can help indicate which meaning of the equal sign is being used.