Week 8 Reading

Introduction

Chapter 16 of the book by Greer, Verschaffel, and De Corte explores how students approach and solve word problems in mathematics. The authors argue that students often suspend their sense-making abilities when solving these problems, influenced by the classroom culture and the implicit rules of the "Word Problem Game."

This chapter examines the attitudes towards word problems from both students and preservice teachers. It finds that both groups share a common belief that mathematical word problems are solely for practicing math skills rather than for solving real-world problems. Consequently, they are often unwilling to consider realistic factors, even when they recognize that the answers seem unrealistic or nonsensical during the process. The authors refer to problems that lack real-life sense-making as P-items and provide examples used in their experiments：

In the experiment, a significant number of both students and preservice teachers provided non-realistic answers to problems containing P-items. One student remarked, "I know all these things, but I would never think to include them in a maths problem. Maths isn't about things like that. It's about getting sums right and you don't need to know outside things to get sums right."

The research suggests that the learning environment shapes students' attitudes toward word problems. Suppose teachers consistently treat word problems as mere assessments in math, without considering real-world factors. In that case, students will develop strategies that focus solely on providing numerical answers without considering realistic contexts.

To address these issues, Greer, Verschaffel, and De Corte propose a reconceptualization of word problems. They suggest designing word problems to better reflect the relationship between mathematics and real-world situations. This approach aims to promote a more meaningful understanding of mathematics and its applications, encouraging students to see the relevance of mathematical concepts in their everyday lives.

Stops

“While there is limited systematic evidence regarding the beliefs of teachers, our

strong impression is that most teachers share the belief that realistic considerations

should not complicate the "real" mathematics that word problems are intended to

evoke. “ (p.278)

 

“there is good reason to assume that teachers' cognitions and beliefs about the role of real-world knowledge in the interpretation and solution of school arithmetic word problems may have strong impact on their actual teaching behavior and, consequently, on their students' learning processes and outcomes.” (p. 282)

 

“at both the level of the school and that of the educational system, assessment is a major agent of belief shaping. Assessment impacts instruction because it transmits powerful signals conveying the goals of instruction, what counts as competence in mathematics, and what forms of mathematical performance are valued.” (p. 286)

 

Reflection

I believe the issue discussed in the article is a common challenge that teachers face during the teaching and learning process. I often ask myself, how are we defining word problems in mathematics? While we frequently say that word problems train students' problem-solving skills or connect academic concepts with students' daily lives, it is questionable whether we are consistently applying this in our daily teaching. The presence of p-items in many problems, whether noticed or not, raises this concern.

I appreciate the discussion about how assessments play a crucial role in shaping beliefs in mathematics. From my perspective, this belief shaping occurs in two ways. First, it relates to the problem itself. Students learn from the teacher's attitude towards considering realistic issues when solving a math problem. When students take assessments, they often care about how to achieve a high mark and how the teacher will grade their answers. Therefore, the teacher's attitude can become part of the rubric communicated in daily teaching. If a teacher does not care about realistic issues or views mathematics word problems as merely testing academic concepts, students will likely adopt the same attitude. They may avoid writing realistic answers to avoid losing marks, opting instead for numerically correct answers.

Second, belief shaping can influence students' broader perception of mathematics. Students might view math class as purely theoretical rather than a tool for solving real-life problems if teachers do not emphasize realistic issues in assessments. This attitude can become ingrained in students from a young age, affecting their approach to math throughout their education.

To address this, we should foster a learning environment that values realistic issues. At the very least, students should know that providing realistic answers in math will not be criticized or considered risky. While teachers may want to test specific mathematical concepts through word problems, it is essential to carefully craft these problems to maintain realism. Mathematics is inherently connected to real life, and there is always a way to test concepts while being realistic.

I also tried to connect this issue with our previous reading from last week, as both address word problems in mathematics. While realism is beneficial, it can sometimes create barriers for ELL or ESL students. These students may struggle to understand the story and provide realistic answers, even if they have sufficient math skills but limited English proficiency. Therefore, we must be cautious about considering realistic answers as the only correct ones, as this can introduce additional linguistic barriers.