Rethinking Parent Involvement: African American Mothers Construct their Roles in the Mathematics Education of their Children

This article presents initial findings from a study that examined how African American mothers from a low-income neighborhood conceptualized their roles in their children’s mathematics learning. Based on interviews and observations focusing on ten mothers’ involvement in their children’s education, we offer a framework that expands typical characterizations of parent involvement. This framework privileges practices that are both traditionally visible and invisible to the school and highlights how parents act as “intellectual resources” in their children’s education (Civil, Guevara, & Allexsaht-Snider, 2002). Our findings offer evidence that traditional understandings of parent involvement may overlook ways that low-income parents deliberately involve themselves in their children’s education. Our findings also identify challenges that these parents face in relation to their children’s mathematics education. Some of these challenges were due in part to stereotypes held by practitioners about the families they serve in low-income urban schools

The Impact of OGAP on Elementary Math Teacher Knowledge and Student Achievement

The Ongoing Assessment Project (OGAP) is a learning trajectory-oriented formative assessment program that develops teachers’ abilities to understand and apply research-based developmental trajectories in math content areas to deepen their thinking about their students. In OGAP, teachers learn to use a learning progression framework to continually assess and adapt their instruction to students’ developing understanding, aiming to move them towards more sophisticated strategies in a range of multiplicative contexts. For this reason, OGAP puts a premium on students’ precision of answer (including correctness and unit labeling) and sophistication of solution response. In this study we examine the multi-year impacts of OGAP on grades 3-5 student correctness and solution sophistication in multiplication on an open-ended assessment created by the Consortium for Policy Research in Education (CPRE) as part of a randomized experimental study of OGAP in Philadelphia schools. In order to assess the intervention’s impact on student learning in both correctness and sophistication, the research team developed an assessment measure with three vertically-equated grade-specific forms composed of open-ended items. The assessment asked students to show their work to allow for analysis of their correctness, strategies, and errors. The results show strong and consistent first year effects on student correctness and solution sophistication multiplication outcomes in all three grades that were assessed. However, these results did not persist during the second year of OGAP treatment, which focused on fraction, when controlling for end of first year results. When examining the second-year multiplication results using the baseline measure, the treatment impacts were present, reinforcing the strength of the first year effects. The next step is to examine year 2 effects in fractions, which was the focus of the second year of OGAP professional development. Additionally, since student and teacher turnover are manifest in Philadelphia, and consequently both students and teachers had different levels of exposure to OGAP, additional analyses are needed to incorporate student and teacher levels of exposure and implementation of OGAP into the models, to disentangle results by level of treatment

Pathways for Analyzing and Responding to Student Work for Formative Assessment: The Role of Teachers’ Goals for Student Learning

This study explored how teachers interpreted and responded to their own student work during the process of formative assessment. The study involved a purposefully selected sample of 32 teachers in grades K-5 who had been trained by the Ongoing Assessment Project (OGAP) to use learning progressions to analyze and respond to evidence in student work. Since formative assessment is fundamentally an interpretive process, involving continually eliciting and interpreting evidence of student thinking from student work in order to inform teaching and learning (Black & Wiliam, 2009), the study analyzed data collected through semi-structured interviews. The study found variations in the way teachers make sense of their student work for formative assessment that were related to their underlying goals for student learning. Teachers with an achievement orientation tended to focus on performance goals: giving formative assessment items to gauge student performance on problems that reflected what had recently been taught and focused on singular or multiple components of performance to make a binary judgment (i.e. students who “get it or don’t get it”). Teachers with a learning orientation gave items to learn more about what students were able to do on different types of problems and focused on student strategies as an indicator of underlying understanding and development. These orientations also had implications for the instructional response teachers developed; as teachers looked beyond surface features of student work and binary distinctions, they developed more differentiated responses that built on students’ knowledge and their ability to develop more sophisticated understanding. In between these two extremes, we found three categories of hybrid approaches to formative assessment, demonstrating a push-and-pull between achievement and learning orientations at different decision points during the steps of the formative assessment process. Those decision points – the teachers’ purpose in giving an item, the evidence focused on, the interpretive framework used to analyze the evidence, and the focus of the instructional responses – offer multiple footholds in the formative assessment process where teachers can begin to try out new approaches that reflect a shift in orientation to student learning. The study shows that using formative assessment is not simply a matter of taking up new practices and using new tools. The variations in understanding and use of the ideas that were offered in professional development, as reflected in teachers’ actual practices, suggests that it is important to provide opportunities for sustained learning and supported use over time

Finnish primary teachers' interaction with curriculum materials - digitalisation as an augmenting element

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School-Based Structures That Support Teacher Use of Learning Trajectory Frameworks

The OGAP intervention incorporates two approaches to mathematics instruction that are well supported by research, but have not been uniformly adopted in U.S. schools: The first is ongoing formative assessment by teachers to tailor instruction to student needs (Black & Wiliam, 1998); the second is the use of learning trajectories to specify conceptual pathways for student development within specific domains (Daro et al., 2011; Sztajn et al., 2012). Implementing OGAP in schools involves a great deal of learning on the part of teachers and school leaders. It also involves embracing a fundamental shift in how one thinks about learning and designing instruction. The OGAP intervention provided grade 3-5 teachers with tools to support learning-trajectory formative assessment practices (described in other papers) and professional development (week- long summer training and several additional training days during the academic year). We also included a site-based approach to increase understanding and capacity across all participating teachers. Each school was asked to hold a bimonthly Professional Learning Community (PLC) with the primary purpose of collaboratively analyzing student work, using learning trajectory frameworks and determining appropriate instructional responses. PLCs were envisioned as a primary structure to support use of OGAP in the schools throughout the year. They were also intended to situate the use of OGAP tools and routines in each school and normalize opportunities for discourse about student thinking among teachers (Putnam & Borko, 2000). By providing teachers with ongoing and consistent opportunities to discuss their own students’ work and use the OGAP frameworks to make instructional decisions, we anticipated they could potentially deepen teachers’ understanding of OGAP and their own students’ thinking. In this paper, we examine five PLCs in the OGAP project in order to consider the extent to which this potential was realized

Experimental Impacts of the Ongoing Assessment Project on Teachers and Students

In this report, we describe the results of a rigorous two-year study of the impacts of a mathematics initiative called Ongoing Assessment Project (OGAP) on teacher and student learning in grades 3-5 in two Philadelphia area school districts. OGAP is a mathematics program which combines teacher formative assessment practices with knowledge of student developmental progressions to build deeper student understanding of mathematics content. OGAP includes teacher professional development, classroom resources, school-based routines for regular practice, and ongoing school-based supports. The study was conducted in 61 schools during the 2014-15 and 2015-16 school years, with OGAP randomly assigned to 31 schools and the remaining 30 serving as comparison sites. The results of this study showed that OGAP produced meaningful impacts on both teacher knowledge and student learning

A cross-cultural study of curriculum systems : mathematics curriculum reform in the U.S., Finland, Sweden, and Flanders

This paper relates to the mathematics curriculum systems of the United States, Finland, Sweden, and Flanders (Belgium). These four regions are in the midst of curriculum reform, which provides interesting grounds for cross-cultural comparison. Our analysis builds on a framework that focuseson curriculum policy, design and enactment in each of these regions and draws on interview data with teachers in all four regions, sample cases of curriculum use, context descriptions, and available descriptions of mathematics education in these four regions. This leads to a more nuanced understanding of the particular curriculum systems through which reform manifests, and sheds light on a challenging balance concerning a curriculum reform that is both coherent across a region and supported by teachers.Peer reviewe