One math improvement trend for 9-year-olds is in use of tables and graphs

Bar chart on chalkboardA good teacher always takes stock of what students already know in order to scaffold instruction on existing understanding.

Curriculum developers at the district, state or national level also need to take stock of what students have learned, what they learn easily and what they learn with difficulty in order to design appropriate curricula.

In a recent study in The Elementary School Journal, Indiana University researcher Peter Kloosterman reviews the performance of 9-year-old students on National Assessment of Education Progress (NAEP) math exams between 1978 and 2004 to find out what students have been learning.

What gains have students made in the last 26 years? The researcher says students made substantial gains in their ability to read and interpret tables and graphs and in calculating perimeter and area. Performance increased on most place-value and computation exam items and was stable on the majority of items involving measurement or money. Students performed poorly on metric items, reflecting the lack of emphasis on this topic in the elementary grades, he notes.

The period of greatest gain

The period of greatest gain for 9-year-olds was 1986-1990 and 1999-2004. The researcher says he is not able to explain the increased gains in these periods. The inclusion of students with disabilities and limited English skills in the 2008 sample, however, makes results in that year and succeeding years, not directly comparable.

“This article makes use of recently released NAEP data to describe what 9-year-old students knew about mathematics in 2004 and how that differs from the knowledge of their counterparts of the 1970s and 1980s,” writes Kloosterman.

One of the items with the greatest gain since 1990 is one that asked students to complete the last 2 bars on a bar graph. In 2003, 73% of grade 4 students correctly completed the last 2 bars compared to 51% in 1990. A possible explanation for the large gains in reading and interpreting tables and graphs could be the increased emphasis on tables and graphs in the elementary school curriculum, the researcher says.

“Tables and graphs are used to display data, and thus essential tools for problem solving, communicating, and reasoning in mathematics,” the researcher writes. “Students probably see more tables and graphs now than their counterparts did in the 1970s, resulting in better performance on tables and graphs items.”

Six content areas

The data set for this study were the 57 items in the age 9 Long-Term Trend database for math assessments of the NAEP between 1978 and 2004. Of the 57 items, 37 were used in all assessments from 1978 through 2004, 15 were used from 1982 through 2004, 3 were used from 1978 through 1999 and 2 items were used from 1982 through 1999. Eighteen of the items were constructed response and the remaining 39 were multiple choice. Constructed response questions were scored as correct or incorrect. There was no partial credit.

The Main NAEP has reported on mathematics performance for individual states and for the country as a whole for grades 4-8 every 2-4 years since 1990. While Main NAEP is constantly changing assessment items, Long-Term Trend (LTT) NAEP used the same items between 1978 and 2004.

The researcher identified 6 content-based clusters of items: Multiplication and division; geometry and measurement; place value and magnitude of whole numbers; addition and subtraction; tables and graphs and money.

Across the full range of items used in 1990, there was statistically significant improvement in only half of the items between 1990 and 2000. There was substantial gain (10% or more) on 27 of the 57 items and gains of at least 6% on 8 more, while there were drops of 6% or more on only 3 items. Over time, students have performed better on items asking for a figure’s perimeter, indicating that far more students have become familiar with the term “perimeter.”

The 57 LTT items represent only a subset of the mathematics skills that 9-year-old students are expected to master. Only 10 of the items were purely computational, although a number of others required application of computational skills (e.g., finding perimeters, making change). The majority of the items involved relatively straightforward mathematical knowledge, such as identifying a place value, interpreting a multiplication sentence, identifying a metric unit, or reading a graph. Main NAEP covers a number of of topics that are not covered by LTT NAEP including questions that involve patterns and different types of measurement and statistics questions.

“In short, although LTT NAEP is limited in comparison to Main NAEP in the content that it covers, it is more than a test of memorized facts and procedures,” he writes.

“Mathemathics skills of nine-year-olds: 1978 to 2004,” by Peter Kloosterman, The Elementary School Journal, 2011, Volume 112, Number 1, pps. 183-203.

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