From curriculum materials to teachers’ enactment of mathematical tasks: A broken telephone game?

Charalambos Charalambous

 

During the past three decades educational research has systematically shown that curriculum tasks play a pivotal role in how much students learn as well as in the quality of their learning. Cognitively demanding tasks, in particular, have been found to promote mathematical reasoning and high-level thinking. Therefore, such tasks have made their way into the mathematics curricula of different countries. Curriculum tasks are, however, not self-enacting. What determines what students learn is how the tasks are implemented during instruction and how students are expected to work on these tasks. In this presentation, we will first consider different types of mathematical tasks, based on their level of cognitive demand, as captured in the Task Analysis Guide. Drawing on the Mathematical Tasks Framework (Stein, Smith, Henningsen, & Silver, 2000), different research findings that document the decline of the cognitive demand of the tasks during enactment will then be summarized. By reflecting on a simulated mathematics lesson, we will next discuss different teaching moves that contribute to such decline. The presentation will conclude by offering ideas that can help maintain the level of cognitive demand, as intended by the curriculum developers (including building on formative assessment as a means of gaining insights into how the tasks are actually enacted by students). In doing so, teachers can ensure, to the extent possible, that the unfolding of tasks in their classrooms does not end up becoming a broken telephone game, in which students get a distorted message—one that is significantly different from that  intended by curriculum developers. 

 

Learning 5 units of mathematics: Crisis or opportunity?

Mohana Fares

 

In this talk, I will present information about students studying the advanced 5-unit mathematics track in high-school, obstacles, and the strategic plan of the Ministry of Education.

 

Implementing formative assessment in mathematics education

Jeremy Hodgen

 

In this talk, I will to examine what formative assessment is and how it can be used to improve students’ understanding of mathematics. I will draw on the findings of research conducted in England, in particular the Increasing Competence and Confidence in Algebra and Multiplicative Structures (ICCAMS) project and earlier work summarized in the booklet for teachers, ‘Mathematics Inside the Black Box’.

 

Making the Fundamental Theorem of Calculus fundamental to calculus

Patrick Thompson

 

My research team at Arizona State University has reconceptualized the calculus curriculum so that students conceptualize accumulation functions (also known as integrals) and rate of change functions (also known as derivatives) as two sides of a coin. We do this by making the Fundamental Theorem of Calculus present in all the ideas that the course develops—from the first day of the course and every day thereafter. I will illustrate how we do this and also illustrate implications for assessment of students’ understandings of calculus, their abilities to reason with them, and will explain how the ways of thinking that students develop in the course prepare them for future mathematical learning.

 

 

Progressive formalization applied: Supporting classroom assessment practices through the development of actionable mathematics knowledge for teaching

David Webb

 

Frameworks that exemplify how students represent and learn mathematics have shown promise for informing teachers’ classroom assessment practices. While much of this research has focused on elementary mathematics, Realistic Mathematics Education and the design principle of progressive formalization offers a generalizable approach in the absence of research-based learning trajectories. This presentation will illustrate how domain-specific problem contexts, representations and strategies can be used by mathematics teachers to reconceptualize mathematical relationships and their interpretation of student responses. Through teachers’ collaborative renegotiation of proposed representational pathways, formative assessment can be examined in ways that support student-centered instruction.