Jennifer Knudsen

Integration of Technology, Curriculum, and Professional Development for Advancing Middle School Mathematics Three Large-Scale Studies

The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum, and teacher professional development. Each study addressed both replicability of findings and robustness across Texas settings, with varied teacher characteristics (backgrounds, knowledge, attitudes) and student characteristics (demographics, levels of prior mathematics knowledge). Analyses revealed statistically significant main effects, with student-level effect sizes of .63, .50, and .56. These consistent gains support the conclusion that SimCalc is effective in enabling a wide variety of teachers in a diversity of settings to extend student learning to more advanced mathematics.

Investigating Links from Teacher Knowledge, to Classroom Practice, to Student Learning in the Instructional System of the Middle-School Mathematics Classroom

Using data collected in 125 seventh-grade and 56 eighth-grade Texas classrooms in the context of the “Scaling Up SimCalc” research project in 2005–07, we examined relationships between teachers’ mathematics knowledge, teachers’ classroom decision making, and student achievement outcomes on topics of rate, proportionality, and linear function—three important and cognitively demanding prealgebra topics. We found that teachers’ mathematical knowledge was correlated with student achievement in only one study out of three. We also found a lack of correlations between teachers’ mathematical knowledge and critical aspects of instructional decision making. Curriculum and other learning resources (e.g., technology, student–student interactions) are clearly important factors for student learning in addition to, and in interaction with, teachers’ mathematical knowledge. Our results suggest that mathematics knowledge for teaching may have a nonlinear relationship with student learning, that those effects may be heavily mediated by other instructional factors, and that short-term content knowledge gains in teacher workshops may not persist in classroom instruction. We discuss a need in the field for richer models of how “mathematical knowledge for teaching” works in the context of complete instructional systems.

From New Technological Infrastructures to Curricular Activity Systems: Advanced Designs for Teaching and Learning

We suggest an “advanced design” for teaching and learning should offer a plan for bridging the gap between new technological affordances and what most teachers need and can use. We draw attention to three different foci of design: (a) design of representational and communicative infrastructure (b) design of curricular activity systems, and (c) design of new classroom practices and routines. Two different SimCalc projects are presented to illustrate these design foci; both concern the use of technology to democratize access to conceptually demanding mathematics among adolescents. We particularly emphasize curricular activity systems because we are finding that attention to this focus of design has been critically important in our ability to measure learning outcomes at the scale of hundreds of teachers.

Scaling up Innovative Technology-Based Mathematics

We report on the initial attempts at evaluating at scale a particular technological/curricular innovation that enables more students to develop deeper knowledge. The methods, issues, and findings of the current pilot experiment speak not only to the success of SimCalc MathWorlds, the focus of our research program, but also to the evaluation at scale of a broad class of representationally innovative technologies and to the merit of long-term investment in design-based research. In particular, we present conditions and findings from a completed pilot experiment involving 21 seventh-grade mathematics teachers from Texas. Pilot outcomes suggest that (a) innovative representational technologies can have an important impact on student learning, (b) considerable impact can be found across a wide range of teachers and conditions, and (c) these gains can be detected even in the absence of other desirable conditions. In particular, detection of student gains does not, in our case, depend on having a long-term context of learning, long-term teacher professional development, or a shift to learner-centered constructivist pedagogy. The full experiment will replicate and extend our experimental design with a wider range of teachers and schools, model the factors that contribute to classroom success with such technology, and explore what happens as research support fades away.

Curricular Activity Systems Supporting the Use of Dynamic Representations to Foster Students’ Deep Understanding of Mathematics

A significant body of research has shown the benefits of dynamic representations technologies for learning. Dynamic representations embed mathematical relationships in objects that can be manipulated and illustrated in a concrete way. An example is a position graph that controls the motion of an object or character (e.g., a person running) in a simulated world. Although the technology required to use dynamic representations is now commonplace their use in the classroom is still limited. This chapter describes the notion of a curricular activity system and how it can be used in the design of learning environments that have a wider reach.

Development of Student and Teacher Assessments in the Scaling Up SimCalc Project

As SimCalc targets mathematics achievement goals that lie beyond what many schools today focus on, new assessments are needed to measure what students learn and what teachers must know to support their learning. We provide an overview of how we developed four assessments for the Scaling Up SimCalc project and describe each of the processes we used to document the technical qualities of the assessments. This methodological approach can be used to measure the effectiveness of dynamic mathematics approaches at scale.