## Introduction

Understanding the abilities of a student goes beyond the confines of classroom instruction. The activities covered in the tutorials agree on the value of one-on-one interviews to students (Clarke, Roche, & Mitchell, 2008; Burns, 2010). Teachers face learning difficulties in teaching fractions to students because of the poor comprehension of its concepts. Studies reveal that the phenomenon exists across junior schools and the college level (Clarke, Roche, & Mitchell, 2008).

Important data from one-on-one interviews reveal insights into tips that teachers can use within the classroom to help students understand mathematic concepts such as fractions. The research-based tips are valuable in classroom activities because of their potential when tested in professional development settings (Clarke, Roche, & Mitchell, 2008). Confidence abounds that these ideas are valuable in making the concept of fractions come alive.

## The value of one-on-one interviews

Burns acknowledges that teachers rely on assignments that students write when assessing their skills and understandings. Burns (2010) asserts that one-on-one interviews aid in revealing information that do not exist when teachers read the works of students. The information is appropriate in tailoring instructional decisions to each student. Burns (2010) points out that this information helps in making appropriate instructional decisions.

Burns states that interviews are the best approaches of learning the mathematical strengths as well as weaknesses of students. With the information, teachers should be able to construct a mathematical profile for every student. The practical experiences reveal the weaknesses of each student, thereby allowing teachers to tailor instructional strategies to their needs (Burns 2010). Rather than rely on student’s writings, one-on-one interviews allow teachers to unearth misunderstandings that they failed to recognize while teaching.

## Misconceptions in learning mathematics

Knowledge of fractions is important to student’s learning of mathematics. Algebra, ratios, percentiles, and proportions makes up the basics of learning measurement (Clarke, Roche, & Mitchell, 2008). Many students have trouble in conceptually understanding these basics. Therefore, probing the thinking of students allows one to understand the misconceptions that result from inappropriately applying a rule about fractions.

According to Clarke, Roche, and Mitchell (2008), mathematics is often neglected where teachers carry out one-on-one assessments in subjects such as reading. Teachers often lack a similar understanding about the ability of students to handle mathematics, a fact that is realized during meetings with students. Fractions define the basis for proportional reasoning and the future of studying mathematics (Clarke, Roche, & Mitchell, 2008). It is noted that various attributes of fractions contribute to the confusion in learning mathematics. One-on-one assessments are useful where teachers are supporting students to help them make sense of a topic, (Clarke, Roche, & Mitchell, 2008). The assessments reveal a depth of understanding about student’s comprehension of the topic.

## The value of proportional reasoning

In the student’s comprehension of place value, Burns (2010) realizes that the language that teachers use in teaching English has a bearing on whether they understand the teacher or not. For instance, reading the number thirteen as ten and three, a verbal pattern existing in Chinese, reveals the role of ten in the whole numbers. The conceptual learning of students is supported by numerous opportunities of counting quantities of objects and noting their exact number.

A teacher should be able to teach students the group of tens and other extra digits in each set of numbers (Burns 2010). Additionally, children may understand a problem, especially when solving addend problems but lack the ability to prove the problem. Burns (2010) asserts that in class, the fingers are an anchor for a student with limited understanding of what they are calculating. Interviews help teachers acknowledge the conceptual foundation for student understanding. Teachers have to help the students develop their number sense. Therefore, it is agreeable that students need time to understand math problems. The ultimate goal of each teacher is developing the proportional reasoning of each student (Burns 2010). Teaching proportional reasoning allows students to sense problems and identify contexts for applying the fractions.

## Conclusions

Where teachers face the dilemma of the appropriate connections that would allow for the easy understanding of mathematics, this paper reveals that one-on-one interviews are a solution. Despite the difficulty in teaching mathematics, assessing the progress of students takes on a central role. Teachers acknowledge that one-on-one interviews are required to understand the student’s comprehension of mathematics.

The understanding of mathematics requires that teachers avail the various problems for representing the fractions, link standard practices to industry benchmarks, and most importantly, gain insight into the student’s thinking through interviews. The interview process allows teachers to respect the attempt by the student to understand mathematical problems. Knowing the misunderstanding of students about mathematical concepts such as fractions is important when addressing the misconceptions that they may have of the subject. It is agreeable that an interview is the solution to the challenges that students face in understanding and learning fraction concepts. The tips that Burns offers are appropriate for helping students understand classroom activities.

## References

Burns, M. (2010). Snapshots of student misunderstandings. *Educational Leadership 67*(5), 18-22.

Clarke, D., Roche, A., & Mitchell, A. (2008). Ten practical tips for making fractions come alive and make sense. *Mathematics Teaching in the Middle School, 13*(7), 373-380.