IES Blog

Institute of Education Sciences

Assessing Math Understanding of Students with Disabilities During a Pandemic

For almost two decades, IES/NCSER has funded Brian Bottge and his teams at the University of Kentucky and University of Wisconsin-Madison to develop and test the efficacy of a teaching method called Enhanced Anchored Instruction (EAI), which helps low-achieving middle school students with math disabilities develop their problem-solving skills by solving meaningful problems related to a real-world problem. The research findings support the efficacy of EAI, especially for students with math disabilities. Most recently, Bottge and his team have been researching innovative forms of assessment that more adequately capture what students with disabilities know both conceptually and procedurally in solving math problems. With supplemental funding, IES/NCSER extended Dr. Bottge’s latest grant to test the use of oral assessment to measure student knowledge and compare that with the knowledge demonstrated on a pencil and paper test. The COVID-19 pandemic introduced added challenges to this work when schools closed and students shifted to online education.

Below we share a recent conversation with Dr. Bottge about the experience of conducting research during a pandemic and what he and his team were still able to learn about the value of oral assessment in mathematics for students with disabilities.

What changes did you observe in the intervention implementation by teachers due to the COVID-related shift to online learning?

The shift to online learning created changes in class size and structure. For 38 days (22 days in classroom, 16 days online through a virtual meeting platform), the middle school special education teacher first taught concepts through a widely used video-based anchored problem, the Kim’s Komet episode of the Jasper Project, in which characters compete in a “Grand Pentathlon.” The teacher then engaged the students in a hands-on application of the concepts by running a live Grand Pentathlon. In the Grand Pentathlon, students make their own cars, race them on a full-size ramp, time them at various release points on the ramp, and graph the information to estimate the speed of the cars. The purpose of both units was to help students develop their informal understanding of pre-algebraic concepts such as linear function, line of best fit, variables, rate of change (slope), reliability, and measurement error. Midway through the study, in-person instruction was suspended and moved online. Instead of working with groups of three to four students in the resource room throughout the day, the teacher provided online instruction to 14 students at one time and scheduled one-on-one sessions with students who needed extra help.

What challenges did you observe in the students interacting with the activities and their learning once they shifted to online learning?

All students had access to a computer at home and they were able to use the online platform without much confusion because they had used it in other classes. The screen share feature enabled students to interact with much of the curriculum by viewing the activities, listening to the teacher, and responding to questions, although they could not fully participate in the hands-on part of the lessons. Class attendance and student behavior were unexpectedly positive during the days when students were online. For example, one student had displayed frequent behavioral outbursts in school but became a positive and contributing member of the online class. The ability to mute mics in the platform gave the teacher the option of allowing only one student to talk at a time.

Were students still able to participate in the hands-on activities that are part of the intervention?

For the hands-on activities related to the Grand Pentathlon competition, the teacher taught online and a research staff member manipulated the cars, track, and electronic timers from campus. Students watched their computer screens waiting for their turn to time their cars over the length of the straightaway. The staff member handled each student’s cars and one by one released them from the height on the ramp as indicated by each student. After students had recorded the times, the teacher asked students to calculate and share the speeds of their cars for each time trial height.

Do you have any other observations about the impact of COVID-19 on your intervention implementation?

One of the most interesting observations was parent participation in the lessons. Several parents went beyond simply monitoring how their child was doing during the units to actively working out the problems. Some were surprised by the difficulty level of the math problems. One mother jokingly remarked: I thought the math they were going to do was as easy as 5 + 5 = 10. The next time my son might have to be the parent and I might have to be the student. You all make the kids think and I like that.

When COVID-19 shut down your participating schools, how were you able to adjust your data collection to continue with your research?

We used the same problem-solving test that we have administered in several previous studies (Figure 1 shows two of the items). On Day 1 of the study (pre-COVID), students took the math pretest in their resource rooms with pencil and paper. Due to COVID-19 school closures, we mailed the posttest and test administration instructions to student homes. On the scheduled testing day during an online class session, students removed the test from the envelope and followed directions for answering the test questions while we observed remotely. On Days 2 and 3 of the study (pre-COVID), an oral examiner (OE) pretested individual students in person. The OE asked the student questions, prompting the student to describe the overall problem, identify the information needed for solving the problem, indicate how the information related to their problem-solving plan, and provide an answer. Due to COVID-19, students took the oral posttests online. The teacher set up a breakout room in the platform where the OE conducted the oral assessments and a second member of the research team took notes.

Figure 1. Sample Items from the Problem-Solving Test

During the testing sessions, the OE projected each item on the students’ computer screens. Then she asked the student to read the problem aloud and describe how to solve it. The OE used the same problem-solving prompts as was used on the pretests. For problems that involved graphs or charts, the OE used the editing tools to make notations on the screen as the students directed. One challenge is that oral testing online made it more difficult to monitor behavior and keep students on task. For example, sometimes students became distracted and talked to other people in their house.

What were the results of this study of oral assessment in mathematics for students with disabilities?

Our results suggest that allowing students to describe their understanding of problems in multiple ways yielded depth and detail to their answers. We learned from the oral assessment that most students knew how to transfer the data from the table to an approximate location on the graph; however, there was a lack of precision due to a weak understanding of decimals. For item 4 in Figure 1, the use of decimals confused students who did not have much exposure to decimals prior to or during the study. We also found that graphics that were meant to help students understand the text-based items were in some cases misleading. The representation in item 4 was different than the actual ramp and model car activity students experienced virtually. We have used this math test several times in our research and regrettably had no idea that elements of the graphics contributed to misunderstanding.

Unfortunately, our findings suggest that the changes made in response to COVID-19 may have depressed student understanding. Performances on two items (including item 4 in Figure 1) that assessed the main points of the intervention were disappointing compared to results from prior studies. The increase in class size from 3–4 to 14 after COVID and switching to online learning may have reduced the opportunity for repetition and practice. There were reduced opportunities for students to participate in the hands-on activities and participate in conversations about their thinking with other students.

We acknowledge the limitations of this small pilot study to compare knowledge of students when assessed in a pencil and paper format to an oral assessment. We are optimistic about the potential of oral assessments to reveal problem-solving insights of students with math disabilities. The information gained from oral assessment is of value if teachers use it to individualize their instruction. As we learned, oral assessment can also point to areas where graphics or other information are misleading. More research is needed to understand the value of oral assessment despite the increase in time it might add to data collection efforts for students with math disabilities. This experience highlights some of the positive experiences of students learning during COVID-19 virtually at home as well as some of the challenges and risks of reduced outcomes from these virtual learning experiences, especially for students with disabilities.

This blog was written by Sarah Brasiel, program officer for NCSER’s Science, Technology, Engineering, and Math program.

New International Data Show Large and Widening Gaps Between High- and Low-Performing U.S. 4th- and 8th-Graders in Mathematics and Science

NCES recently released results from the 2019 Trends in International Mathematics and Science Study (TIMSS). TIMSS tests students in grades 4 and 8 in mathematics and science every 4 years. The results show that

  • Across both subjects and grades, the United States scored, on average, in the top quarter of the education systems that took part in TIMSS 2019.
    • Among the 64 education systems that participated at grade 4, the United States ranked 15th and 8th in average mathematics and science scores, respectively.
    • Among the 46 education systems that participated at grade 8, the United States ranked 11th in average scores for both subjects.
  • On average, U.S. scores did not change significantly between the 2011 and 2019 rounds of TIMSS.

Average scores are one measure of achievement in national and international studies. However, they provide a very narrow perspective on student performance. One way to look more broadly is to examine differences in scores (or “score gaps”) between high-performing students and low-performing students. Score gaps between high performers and low performers can be one indication of equity within an education system. Here, high performers are those who scored in the 90th percentile (or top 10 percent) within their education system, and low performers are those who scored in the 10th percentile (or bottom 10 percent) within their education system.

In 2019, while some education systems had a higher average TIMSS score than the United States, none of these education systems had a wider score gap between their high and low performers than the United States. This was true across both subjects and grades.

Figure 1 shows an example of these findings using the grade 8 mathematics data. The figure shows that 17 education systems had average scores that were higher or not statistically different from the U.S. average score.

  • Of these 17 education systems, 13 had smaller score gaps between their high and low performers than the United States. The score gaps in 4 education systems (Singapore, Chinese Taipei, the Republic of Korea, and Israel) were not statistically different from the score gap in the United States.
  • The score gaps between the high and low performers in these 17 education systems ranged from 170 points in Quebec, Canada, to 259 points in Israel. The U.S. score gap was 256 points.
  • If you are interested in the range in the score gaps for all 46 education systems in the TIMSS 2019 grade 8 mathematics assessment, see Figure M2b of the TIMSS 2019 U.S. Highlights Web Report, released in December 2020. This report also includes these results for grade 8 science and both subjects at the grade 4 level.

Figure 1. Average scores and 90th to 10th percentile score gaps of grade 8 students on the TIMSS mathematics scale, by education system: 2019

NOTE: This figure presents only those education systems whose average scores were similar to or higher than the U.S. average score. Scores are reported on a scale of 0 to 1,000 with a TIMSS centerpoint of 500 and standard deviation of 100.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2019.


From 2011 to 2019, U.S. average scores did not change significantly. However, the scores of low performers decreased, and score gaps between low and high performers grew wider in both subjects and grades. In addition, at grade 8, there was an increase in the scores of high performers in mathematics and science over the same period. These two changes contributed to the widening gaps at grade 8.

Figure 2 shows these results for the U.S. grade 8 mathematics data. Average scores in 2011 and 2019 were not significantly different. However, the score of high performers increased from 607 to 642 points between 2011 and 2019, while the score of low performers decreased from 409 to 385 points. As a result, the score gap widened from 198 to 256 points between 2011 and 2019. In addition, the 2019 score gap for grade 8 mathematics is significantly wider than the gaps for all previous administrations of TIMSS.


Figure 2. Trends in average scores and selected percentile scores of U.S. grade 8 students on the TIMSS mathematics scale: Selected years, 1995 to 2019

* p < .05. Significantly different from the 2019 estimate at the .05 level of statistical significance.

NOTE: Scores are reported on a scale of 0 to 1,000 with a TIMSS centerpoint of 500 and standard deviation of 100.

SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 1995, 1999, 2003, 2007, 2011, 2015, 2019.


These TIMSS findings provide insights regarding equity within the U.S. and other education systems. Similar results from the National Assessment of Educational Progress (NAEP) show that mathematics scores at both grades 4 and 8 decreased or did not change significantly between 2009 and 2019 for lower performing students, while scores increased for higher performing students. More national and international research on the gap between high- and low-performing students could help inform important education policy decisions that aim to address these growing performance gaps.

To learn more about TIMSS and the 2019 U.S. and international results, check out the TIMSS 2019 U.S. Highlights Web Report and the TIMSS 2019 International Results in Mathematics and Science. A recording is also available for a RISE Webinar from February 24, 2021 (What Do TIMSS and NAEP Tell Us About Gaps Between High- and Low-Performing 4th and 8th Graders?) that explores these topics further. 

 

By Katie Herz, AIR; Marissa Hall, AIR; and Lydia Malley, NCES

New International Data Identify “Resilient” Students in Financial Literacy

NCES recently released the results of the Program for International Student Assessment (PISA) 2018 assessment of financial literacy. This assessment measured 15-year-old students’ knowledge and understanding of financial concepts, products, and risks and their ability to apply that knowledge to real-life situations. It found that, on average, U.S. students performed similarly to their peers across the 12 other participating Organization for Economic Cooperation and Development (OECD) countries. 

The assessment also found that 12 percent of U.S. students performed at the highest level of proficiency (level 5). Performance at this level indicates that students can apply their understanding of financial terms and concepts to analyze complex financial products, solve nonroutine financial problems, and describe potential outcomes of financial decisions in the big picture.[1] The U.S. percentage was again similar to the OECD average.

However, this analysis also identified a group of students who might be considered “resilient.” In education research, resilience is defined as the ability to perform well academically despite coming from the disadvantaged backgrounds that have more commonly been associated with lower performance.

High-performing students came from across the spectrum of school poverty levels, as measured by the percentage of students eligible for free or reduced-price lunch (FRPL).[2] In particular, 7 percent of high-performing students in financial literacy came from the highest poverty schools (figure 1).


Figure 1. Percentage distribution of U.S. 15-year-olds in public schools scoring below level 2 and at level 5 of proficiency on the PISA financial literacy scale, by percentage of students eligible for free or reduced-price lunch (FRPL) at their school: 2018

NOTE: Data for percentage of students eligible for FRPL were available for public schools only. An individual student’s level of poverty may vary within schools. Detail may not sum to totals due to rounding.

SOURCE: Organization for Economic Cooperation and Development (OECD), Program for International Student Assessment (PISA), 2018.


It is these 7 percent of students who could be considered “resilient” and may be of interest for further study. For example, research could identify if there are factors that are associated with their high performance when compared to their lower performing peers in similar schools. Research on academically resilient students that used eighth-grade data from TIMSS found, for example, that having high educational aspirations increased the likelihood that students with few home education resources performed at or above the TIMSS Intermediate international benchmark in mathematics.[3] Experiencing less bullying also increased this likelihood.

Examining the “resilient” PISA financial literacy students more closely could also determine the extent to which their individual backgrounds are related to performance. This would be of interest because, even within high-poverty schools, students’ individual circumstances may vary. 

Patterns in Other PISA Subjects

There are similar subsets of “resilient” students in the other PISA 2018 subjects (table 1). Eight percent of high performers in reading were from the highest poverty schools, as were 5 percent of high performers in mathematics and 7 percent of high performers in science.


Table 1. Percentage of U.S. 15-year-olds in public schools scoring at or above level 5 of proficiency, by PISA subject and their schools’ free or reduced-price lunch (FRPL) status: 2018

[Standard errors appear in parentheses]

NOTE: Results are scaled separately; thus, percentages cannot be compared across subjects. Level 5 is the highest level of proficiency in financial literacy; levels 5 and 6 are the highest levels of proficiency in the other PISA subjects. Data for students eligible for FRPL were available for public schools only.

SOURCE: Organization for Economic Cooperation and Development (OECD), Program for International Student Assessment (PISA), 2018.


For more information on the PISA 2018 results in financial literacy and other subjects, visit the NCES International Activities website. To create customized data and charts using PISA and other international assessment data, use the International Data Explorer.

 

By Maria Stephens, AIR


[2] Data for students eligible for FRPL are available for public schools only.

[3] Students at the Intermediate international benchmark can apply basic mathematical knowledge in a variety of situations, and those above this benchmark can do so in increasingly complex situations and, at the highest end, reason with information, draw conclusions, make generalizations, and solve linear equations.

NCES Releases First-Ever Response Process Dataset—A Rich New Resource for Researchers

The NCES data file National Assessment of Educational Progress (NAEP) Response Process Data From the 2017 Grade 8 Mathematics Assessment (NCES 2020-102; documentation NCES 2020-134) introduces a new type of data—response process data—which was made possible by NAEP’s transition from paper to digitally based assessments in mathematics and reading in 2017. These new datasets allow researchers to go beyond analyzing students’ answers to questions as simply right or wrong; instead, researchers can examine the amount of time students spend on questions, the pathways they take through the assessment sections, and the tools they use while solving problems. 

NAEP reporting has hinted previously at the promise of response process data. With the release of the 2017 mathematics assessment results, NCES included a feature on The Nation’s Report Card website to show the different steps students took while responding to a question that assessed their multiplication skills. The short video below shows that students used a total of 397 different sequences to group four digits into two factors that yield a given product. The most popular correct and incorrect answer paths are shown in the video. Response process data, such as those summarized in this example item, can open new avenues for understanding how students work through math problems and identifying more detailed elements of response processes that could lead to common math errors.



In the newly released data, researchers can access student response process data from two 30-minute blocks of grade 8 mathematics assessment questions (or a total of 29 test items) and a 15-minute survey questionnaire where students responded to questions about their demographic characteristics, opportunities to learn in and outside of school, and educational experiences. Researchers can explore logs of the response process data collected from each student along with a file containing students’ raw responses and scored responses, time stamps, and demographics. In addition, researchers can explore a file that summarizes defined features of students’ interactions with the assessment, such as the number of seconds spent on specific questions or the number of times the calculator was opened across all students.

To explore this response process dataset, interested researchers should apply for a restricted-use license and request access to the files through the NCES website. By providing this dataset to a wide variety of researchers, NCES hopes to encourage and enable a new domain of research on developing best practices for the use and interpretation of student response process data.

 

By Jan Marie Alegre and Robert Finnegan, Educational Testing Service

NAEP Opens a Pathway to Exploring Student Problem Solving in Assessments

A newly released NCES First Look report, Response Process Data From the NAEP 2017 Grade 8 Mathematics Assessment (NCES 2020-068), introduces a new type of data—response process data—which was made available after the NAEP reading and math assessments transitioned from paper to digitally based assessments in 2017. These new datasets will allow researchers to go beyond analyzing students’ answers to questions as simply right or wrong; instead, researchers will be able to examine the amount of time students spend on questions, the pathways they take through the assessment sections, and the tools they use while solving problems. The new First Look report provides an overview of data that will be available when the restricted-use data files for the 2017 grade 8 mathematics response process data are released later this summer.

NAEP reporting has hinted previously at the promise of response process data. With the release of the 2017 mathematics assessment results, NCES included a feature on The Nation’s Report Card website to show the different steps students took while responding to a question that assessed their multiplication skills. The short video below shows that students used a total of 397 different sequences to group four digits into two factors that yield a given product. The most popular correct and incorrect answer paths are shown in the video. Response process data, such as those summarized in this example item, can open new avenues for understanding how students work through math problems and identifying more detailed elements of response processes that could lead to common math errors.



The First Look report describes the forthcoming data files that will enable researchers to access student response process data from two 30-minute blocks of grade 8 mathematics assessment questions (or a total of 29 test items) and a 15-minute survey questionnaire where students responded to questions about their demographic characteristics, opportunities to learn in and outside of school, and educational experiences. Researchers will be able to explore logs of the response process data collected from each student along with a file containing students’ raw responses and scored responses, time stamps, and demographics. In addition, researchers can explore a file that summarizes defined features of students’ interactions with the assessment, such as the number of seconds spent on specific questions or the number of times the calculator was opened across all students.

To explore this response process dataset, interested researchers should apply for a restricted-use license and request access to the files through the NCES website. By providing this dataset to a wide variety of researchers, NCES hopes to encourage and enable a new domain of research on developing best practices for the use and interpretation of student response process data.

 

By Jan Marie Alegre and Robert Finnegan, Educational Testing Service