Abstract

In this study, we explored the insights that Chinese primary mathematics teachers gained into their students’ mathematical understanding from using classroom assessment techniques (CATs). CATs are short teacher-initiated targeted assessment activities proximate to the textbook, which teachers can use in their daily practice to make informed instructional decisions. Twenty-five third-grade teachers participated in a two-week program of implementing eight CATs focusing on the multiplication of two-digit numbers, and filled in feedback forms after using the CATs. When their responses described specific information about their students, emphasized the novelty of the gained information, or referred to a fitting instructional adaptation, and these reactions went together with references to the mathematics content of the CATs, the teachers’ responses were considered as evidence of gained insights into their students’ mathematics understanding. This was the case for three-quarters of the teachers, but the number of gained insights differed. Five teachers gained insights from five or more CATs, while 14 teachers did so only from three or fewer CATs, and six teachers showed no clear evidence of new insights at all. Despite the differences in levels of gained insights, all the teachers paid more attention to descriptions of students’ performance than to possible instructional adaptations.

Highlights

  • In which classroom assessment techniques (CATs) for primary mathematics education were developed and teachers were supported in using CATs, we investigated the use of CATs in China

  • Gaining insights here means that clear indications could be identified in a teacher’s response to a particular CAT: that the teacher referred to specific information about his/her students, or emphasized the novelty of the gained information, or referred to a fitting instructional adaptation, and these reactions went together with references to the mathematics content of the CATs

  • Three teachers (S03, S13, N06) seemed not to understand what CAT-8 aims to assess. They thought that the assessed mathematical content was students’ ability to apply the properties of multiplication; for example “it is difficult for students to understand the distributive property” (S13)

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Summary

Assessment in the Hands of Teachers

Any instructional decision making—and any form of teaching—requires in one way or another information about students’ learning [1]. The more reliable and valid this information is, the better teachers can find a foothold for these decisions For generating such information, many approaches are possible, ranging from standardized externally developed tests to teacher-made assignments. Other measures that make assessments by teachers more informative are using rubrics [14] or concept maps [15] as frameworks for analyzing students’ responses. Both measures were found to assist teachers in identifying gaps in their students’ understanding of the particular mathematical topics under investigation

Assessment Techniques
A New Approach to Assessment in Mathematics Education in China
The Present Study
Methods
Participants
Exercises
Multiplication
CATs for Assessing Multiplication of Two-Digit Numbers
CAT-1: CAT-1
CAT-3: CAT-3
CAT-4: CAT-4
CAT-8: CAT-8
CAT-8: Solving Problems without Algorithm
Teacher
Data Analysis
Teachers Gaining Insights from Using the CATs
Insights from Using CAT-1
Insights from Using CAT-3
Insights from Using CAT-4
Insights from Using CAT-8
Conclusions and Discussion
The eight of two-digit numbers
Full Text
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