The power of feedback.

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Methods in Educational Research: From Theory to Practice

McKenney, S. (2012, 4-5 September). What is educational design research? Invited lecture for the Crossfield Graduate School at the University of St. Gallen, St. Gallen, Switzerland.

What is educational design research

A randomized-trials design was used to evaluate the effectiveness of a preschool mathematics program based on a comprehensive model of researchbased curricula development. Thirty-six preschool classrooms were assigned to experimental (Building Blocks), comparison (a different preschool mathematics curriculum), or control conditions. Children were individually pre- and posttested, participating in 26 weeks of instruction in between. Observational measures indicated that the curricula were implemented with fidelity, and the experimental condition had significant positive effects on classrooms’ mathematics environment and teaching. The experimental group score increased significantly more than the comparison group score (effect size = 0.47) and the control group score (effect size = 1.07). Early interventions can increase the quality of the mathematics environment and help preschoolers develop a foundation of mathematics knowledge.

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Experimental Evaluation of the Effects of a Research-Based Preschool Mathematics Curriculum:

This study employed a cluster randomized trial design to evaluate the effectiveness of a research-based intervention for improving the mathematics education of very young children. This intervention includes the Building Blocks mathematics curriculum, which is structured in research-based learning trajectories, and congruous professional development emphasizing teaching for understanding via learning trajectories and technology. A total of 42 schools serving low-resource communities were randomly selected and randomly assigned to 3 treatment groups using a randomized block design involving 1,375 preschoolers in 106 classrooms. Teachers implemented the intervention with adequate fidelity. Pre- to posttest scores revealed that the children in the Building Blocks group learned more mathematics than the children in the control group (effect size, g = 0.72). Specific components of a measure of the quantity and quality of classroom mathematics environments and teaching partially mediated the treatment effect.

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Mathematics Learned by Young Children in an Intervention Based on Learning Trajectories: A Large-Scale Cluster Randomized Trial

Ten key principles from research for the professional development of mathematics teachers

Este libro trata sobre la seleccion y el uso de tareas que pueden facilitar el aprendizaje de las matematicas. Se centra en las elecciones de tareas que realizan los profesores y las acciones que realizan al utilizar las tareas. Describe tareas que pueden usarse para facilitar el aprendizaje de las matematicas y pueden hacer que la experiencia de aprender matematicas sea atractiva y gratificante y que la ensenanza de las matematicas sea satisfactoria. Se basa en los hallazgos de un proyecto particular que investiga el uso de tareas matematicas y tambien en nuestros proyectos de investigacion anteriores y en nuestra experiencia en el trabajo con profesores de matematicas potenciales y en ejercicio.

Teaching with Tasks for Effective Mathematics Learning

The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers responded to survey items in both Likert and free format style after teaching the ten lessons. The responses of the teacher participants indicate that the lesson structure we proposed was helpful, and the elements of the lessons suggested to teachers were both necessary and sufficient for supporting students in engaging with the challenging tasks. Implications for teacher educators and curriculum developers are offered.

Supporting teachers in structuring mathematics lessons involving challenging tasks

As part of a research and professional development project that focused on the opportunities and constraints provided by different kinds of mathematical tasks, a group of 67 primary and 40 secondary practising teachers of mathematics were asked to complete a survey focusing on their use of tasks. In this article, we discuss responses to one particular item which sought teachers’ ideas on taking a fraction comparison task (which is larger: 2/3 or 201/301?) and converting it into a mathematics lesson in the middle years of schooling. Drawing upon a number of components of ‘mathematical knowledge for teaching’ as a framework, we attempt to examine those aspects of mathematical knowledge which are involved in making such a conversion. Our recommendation following this analysis is that greater emphasis is necessary in professional development settings on taking a potentially useful task and converting it into a worthwhile mathematics learning experience for students. Knowing the relevant mathematics also seems necessary even if not sufficient to make this conversion.

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Douglas McLean Clarke

Papers

Ten key principles from research for the professional development of mathematics teachers

Teaching with Tasks for Effective Mathematics Learning

Supporting teachers in structuring mathematics lessons involving challenging tasks

Converting Mathematics Tasks to Learning Opportunities: An Important Aspect of Knowledge for Mathematics Teaching.

Mathematics teaching in grades K-2: painting a picture of challenging, supportive, and effective classrooms