Improved Mathematical Teaching Learning Using Complex Performance Assessment Tasks

Summary:  This paper studied the potential of using complex performance tasks to improve teaching practices and students' mathematics performance within and across years. This twelve-year longitudinal analysis across 35 districts shows that use of the MARS tasks improves teachers' pedagogy and students' mathematical learning on performance tasks and statewide assessments.

Perspectives

The Common Core State Standards (CCSS) call for a substantial increase in the breadth and depth of mathematical knowledge students must acquire to be college and career ready. Unfortunately, few districts have the capacity to help their students meet these rigorous requirements. National and state-level reports document critical shortages and high attrition in the overall supply of appropriately trained and certified mathematics teachers (National Science Board, 2006). Additionally, the majority of secondary mathematics teachers lack deep knowledge of the content they are expected to teach (Barth & Haycock, 2004; Massell, 1998).

Research also shows inconsistencies in instruction across classrooms within the same district and even within the same school. Teachers interpret the same instructional ideas in various ways (Marzano, 2003; Stigler & Hiebert, 1998; 1999), and accordingly make independent decisions about how to ignore, adapt, or adopt recommendations for instruction (Spillane, Reiser, & Reimer, 2002). As such, mathematics instruction has proven very difficult to improve (Bamburg, 1994; Beck-Winchatz & Barge, 2003) and students are not given adequate opportunity to succeed in challenging mathematics (National Science Board, 2006).

Despite substantial investments in professional development, evidence of their effectiveness varies greatly in quality and usefulness. Given the upcoming transition to the CCSS, it is important to identify effective resources that provide guidance to teachers on next steps in their teaching practices. The use of complex performance tasks is touted as critical in the two assessment consortia, and as a result, there is high need to find ways to transition teachers' use of these new assessment types as well as ways to build their capacity to use that information to truly improve their teaching and thus student learning.

Description of the Practice

The Silicon Valley Mathematics Assessment Collaborative (MAC) was created to provide richer assessment information for teachers, schools, and districts to use to inform instruction, since statewide assessment data did not provide the information practitioners needed to make changes in the classroom. Using the recommendations from NCTM, MAC outlined five core topics at each grade level they thought were worthy of teachers' efforts, of sufficient scope to allow for deep student thinking, and able to be assessed on an exam that lasted a single class period.

The Mathematics Assessment Resource Service (MARS) exam is a performance assessment consisting of five tasks that assess concepts and skills at each grade level in addition to problem solving, reasoning, and communication skills. The tasks require students to evaluate, optimize, design, plan, model, transform, generalize, justify, interpret, represent, estimate, and calculate their solutions. Each MARS task is assigned a point total that corresponds to the task complexity, how the students approach the problem, to the core of the performance, and evidence that, beyond finding a correct solution, students demonstrate the ability to justify or generalize their solutions.

The combination of constructed-response tasks and weighted rubrics provides a detailed picture of student performance and how students approached the different tasks, with a description of common misconceptions and evidence of what students understand. Reports include student work samples at each grade level showing the range of approaches, successes, and challenges. The reports also provide implications for instruction, giving specific suggestions and ideas for teachers as a result of examining students' strengths and the areas where more learning experiences are required.

This wealth of resources provides a structure for teachers to study student understanding and misconceptions as evidence to help inform and adjust future instruction. By focusing on these detailed and structured analyses of student work on complex tasks, teachers can get a better sense of what students understand or what skills still need to be developed.

Data Sources and Methods

The data includes 12 years of assessments, matching both teachers and students across the years: teacher experience in MAC, performance of their students on the MARS tasks and statewide assessments, and demographic information for teachers and students.

We began with exploratory analyses using analysis of variance, where student performance on the MARS and statewide assessment were used as dependent variables, disaggregated by teacher experience in MAC, years teaching, and other demographic information within a single year. We then conducted some preliminary analyses looking across years to see how students' mathematical performance (as seen on both MARS and the statewide assessment) changed when they were taught by teachers using the MARS resources for examining student learning.

Results

Use of the MARS tasks shows promise for improving teachers' pedagogy and students' mathematical learning. Qualitative results show that teachers are better equipped for understanding what their students know and how to shape and reshape their instruction accordingly. Teachers spend more time talking about student work and find evidence of what students have learned rather than use anecdotal information to gauge students' understanding (Paek, 2008).

Table 1 shows the pass rates on a large-scale mathematics assessment. Teachers who engaged in MAC had a higher percentage of students passing the statewide assessment than those who did not. The differences in results are significant for all four grades

[Insert Table 1]

The longer students were involved in classrooms with MAC teachers, the more likely they were to meet the performance standards on MARS. Figure 1 provides an example of the performance of a cohort of students in grades 4–7 on MARS taught by MAC teachers. Before teachers were involved in MAC, only 30% of students met the standards, compared with almost 100% of students with MAC teachers for three years.

[Insert Figure 1]

Educational Importance

Transition to the CCSS includes a shift in instruction and types of assessments. As a result, the field needs to understand what teacher support around studying complex performance tasks has proven successful for promoting positive changes to teaching and learning. The MARS tasks are in line with the two assessment consortia's descriptions of must-needed performance tasks, so better understanding the data and impact on teaching and learning is paramount for informing the pragmatic decisions that will be made in the upcoming years around what types of mathematics tasks assess deeper student learning AND reflect improved teaching practices.

References

Bamburg, J. (1994). Raising expectations to improve student learning. Oak Brook, Illinois: North Central Regional Educational Laboratory.

Barth, P., & Haycock, K. (2004). A core curriculum for all students. In R. Kazis, J. Vargas, & N. Hoffman (Eds.). Double the numbers: Increasing postsecondary credentials for underrepresented youth (pp. 35-45). Cambridge, MA: Harvard Education Press.

Beck-Winchatz, B. & Barge, J. (2003). A new graduate space science course for urban elementary and middle school teachers at DePaul University in Chicago. The Astronomy Education Review, 1(2), 120–128.

Marzano, R. J. (2003). What works in schools: Translating research into action. Alexandria, VA: Association for Supervision and Curriculum Development.

Massell, D. (1998). State strategies for building local capacity: Addressing the needs of standards-based reforms. Philadelphia, PA: Center for Policy Research in Education, University of Pennsylvania.

National Science Board. (2006, January). America's pressing challenge: Building a stronger foundation. NSB 06-02. Washington, DC: Author.

Paek, P. L. (2008, January). Mathematics coaching: Silicon Valley Mathematics Initiative. Case study from Practices worthy of attention: Local innovations in strengthening secondary mathematics. Austin, TX: Charles A. Dana Center at The University of Texas at Austin.

Spillane, J., Reiser, B., & Reimer, T. (2002). Policy implementation and cognition: Reframing and refocusing implementation research. Review of Educational Research, 72, 387–431.

Stigler, J. W., & Hiebert, J. (1998, Winter). Teaching is a cultural activity. American Educator. Retrieved March 14, 2007, from http://www.aft.org/pubs-reports/american_
educator/winter98/index.html.

Stigler, J. W., & Hiebert, J. (1999). The teaching gap: Best ideas from the world's teachers for improving education in the classroom. New York: Free Press.

Table 1. Pass Rates on the Mathematics Portion of the Statewide Assessment

Figure 1. Percentage of Students Passing MARS Based on Length of Time with MAC Teachers