‘Negative of my money, positive of her money’: secondary students’ ways of relating equations to a debt context

Abstract

We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways. Many students represented the situation numerically without invoking negative numbers, whereas others wrote equations involving negative numbers. When asked to interpret equations involving negative numbers in relation to the story, students did so in two ways. Their responses reflect distinct perspectives concerning the relationship between arithmetic equations and borrowing/owing. We discuss these findings and their implications regarding the role of contexts in integer instruction.

Examining Pinterest as a Curriculum Resource for Negative Integers: An Initial Investigation

“…Similarly, the near absence of real-world context suggests that problems and activities involving real-life situations are not of value. However, real-world contexts are foundational knowledge for reasoning about negative integers [11]. Overall, the results show that the curriculum of Pinterest related to negative integers lacks the depth found in the curriculum of textbooks [30,31].…”

“…Our choice to investigate negative integer resources available on Pinterest is intentional and based on knowledge of the difficulties associated with teaching and learning about integers, which have been shown to be notoriously challenging for all [8][9][10][11]. Specific challenges with integers include a focus on procedures [12], difficulty with subtraction [13,14], and language issues [11,15].…”

“…Specific challenges with integers include a focus on procedures [12], difficulty with subtraction [13,14], and language issues [11,15]. Although research has shown that young children are capable of reasoning with integers [16][17][18][19], there are many examples of adults struggling with the content.…”

“…Likewise, Bofferding and Richardson [12] illustrated that preservice teachers often focus on procedures when solving integer addition and subtraction problems. Recent research has also pointed to the difficulties that secondary students have connecting integers and contexts [11]. Drawing on a historical lens, mathematicians in the 1700s and 1800s modeled integer addition and subtraction on a number line, but struggled to do the same for integer multiplication and division [8].…”

“…Additionally, language presents challenges when working with integers. For example, identifying whether money referenced in a contextualized problem with integers is viewed from the perspective of the lender or borrower of the money [11]. Similarly, it is challenging for students to coordinate what the words "more" or "less" mean with integers [15].…”