Mathematics Assessments
From APEC HRDWG Wiki
Assessments identify the mathematics content that is most valued for student learning. Just as important as mathematics standards and instructional practices, assessing learning is a hallmark of effective instruction. Summative assessments at particular grades measure students' mathematics learning for purposes of student, teacher, or school accountability. Formative assessments given throughout the school year provide feedback on student mastery of recently taught content and are useful for teachers in guiding instruction.
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Sample Assessment Items
The APEC mathematics assessment database provides sample assessment items. This data base is part of a newly started United States project to collect sample items from summative assessments of APEC member economies. Each assessment item is reported by mathematics strand and by percentage of students answering the item correctly, which serves as an indicator of item difficulty. View the assessment database that includes the assessment items from the following sources:
- United States: Massachusetts (2007 Massachusetts Comprehensive Assessment System)
- Japan: (Assessments for grades 6 and 9)
- China: Hong Kong: (2007 Assessments for grades 3 and 9)
- New Zealand: (2007 Secondary School Assessments)
The Massachusetts assessment was selected because students from that state consistently perform better than students from any other state on the National Assessment of Educational Progress (NAEP). However, a comparison of the Massachusetts and Hong Kong Assessment shows there is work still to be done in the U.S. An analysis of the assessments revealed that items on the Japanese assessment are more mathematically challenging than those on Massachusetts assessment. The most difficult problem on the Massachusetts assessment was a number line problem. The Full Assessment Materials are available on a separate Wiki page, as are Overviews of Assessments found in the Database.
Examples:
For the same grade (6th), the Japanese assessment questions appear to include items that are more mathematically challenging than Massachusetts assessment questions when analyzed by percent of test takers answering the question correctly.
To illustrate, in the example below, the most difficult Massachusetts problem with only about 25 percent answering correctly is a number line problem that challenges the student to recognize that the number line is marked off in thirds and then to perform a straightforward computation of 4 1/3 -1 2/3 = 2 2/3. Only 26 percent of Massachusetts sixth graders taking the assessment in 2007 gave the correct response to this item.
- Massachusetts Grade 6 (2007) ---most difficult problem (26% correct)
Items: Using the number line below, what is the distance between point A and point B?
Ans. 2 2/3 fraction or equivalent.)
The Japanese example below is a much more conceptually demanding multi-step geometric math problem. A student must use map-reading skills, know the formulas for the areas of rectangles and parallelograms, use rules about parallel lines, and perform multi-digit multiplication. The problem also includes distracters that is, numbers not required to solve the problem. Correctly Answering this problem requires a much greater application of mathematical thinking, conceptual understanding,and procedural knowledge than the single step Massachusetts difficult problem. Eighteen percent of Japanese sixth-grade students answered this item correctly.
- Japanese Grade 6 ---most difficult problem (18% correct)
Items:There are two parks close to Hiroshi’s house, as shown in the map below. Which
park has the larger area, Central Park or East Park? Write your answer and the reason
for, your answer using words and mathematical expressions.
