Mathematics Teacher Circles Around Mathematics - An article about Math Teacher Circles by Anthony Fernandes, Jacob Koehler, and Harold Reiter, published in the Sept. 2011 issue of NCTM's"Mathematics Teaching in the Middle School"

Improving Learning in Mathematics: Challenges and Strategies - Malcolm Swam

Math Assessment Project Professional Development Modules

• To truly meet the demands of the Common Core State Standards it is not sufficient to simply revise the list of mathematical content covered in the curriculum. The Standards' emphasis on Mathematical Practices require students to be able to think mathematically, and apply the techniques they have learned to rich problems in diverse contexts. Achieving this requires changes in the way mathematics is taught and assessed in most schools.
• The Mathematics Assessment Project has developed the Classroom Challenges to exemplify the types of activities needed to supplement traditional classroom practice and support the Standards. The Professional Development Modules are designed to help teachers with the practical and pedagogical challenges presented by these lessons.
• Module 1 intoduces the model of formative assessment used in the lessons, its theroetical background and practical implemention. Modules 2 & 3 look at the two types of Classroom Challenges in detail. Modules 4 & 5 explore two crucial pedagogical features of the lessons: asking probing questions and collaborative learning.
• The modules are activity-based; built around a collection of example classroom activities. The aim is to engage groups of teachers in constructive discussions about their own practices and how these could change. They then plan and teach a lesson using these ideas in their own classroom, and meet again to reflect on their experiences.
• Each module includes a PD session guide and handouts for teachers, as well as sample classroom materials and suggested lesson plans. Also included are videos of real teachers trying these techniques with their own classes, often for the first time, and discussing the results.

• Formative Assessment - "How can I respond to students in ways that improve their learning?"  

Professional development materials created by the Math Assessment Project (MAP) at the Shell Center.  Mathematics teaching assumes that students do not arrive at sessions as ‘blank slates’, but as actively thinking people with a wide variety of skills and conceptions. Research shows that teaching is more effective when it assesses and uses prior learning so that the teaching may be adapted to the needs of students (Black & Wiliam, 1998). Prior learning may be uncovered through any activity that offers students opportunities to express their understanding and reasoning. It does not require more testing. For example, it can take the form of a single written question given at the beginning of a session to elicit a range of explanations that may then be discussed. This process, often referred to as formative assessment, may be defined as: "… all those activities undertaken by teachers, and by their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs. (Black & Wiliam, 1998).  This module considers the different ways this can be done and focuses on the following questions:

•  How can problems be used to assess performance?
•  How can this assessment be used to promote learning? 
•  What kinds of feedback are most helpful for students and which are unhelpful?
•  How can students become engaged in the assessment process?

• Problem-Solving Lessons - "Do I stand back and watch or intervene and tell them what to do?"

 Professional development materials created by the Math Assessment Project (MAP) at the Shell Center.  Problem Solving lessons are intended to assess and develop students’ capacity to select and deploy their mathematical knowledge in non-routine contexts and typically involve students in comparing and critiquing alternative approaches to solving a problem. This PD module, focuses on Problem Solving lessons. In most Mathematics classrooms, students are provided with structured tasks and are told precisely which techniques to use: students learn by following instructions. Even tasks described as ‘problem solving’ often amount to mathematical exercises rephrased in ‘plain English’, with a well-defined ‘correct’ solution method. Problems and situations that arise in the world, however, are rarely exercises in the use of a particular skill or concept. Such problems require students to make simplifications, model situations, choose appropriate knowledge and processes from their ‘toolkit’, and test whether their solution is ‘good enough’ for the purpose in hand. If students are to learn to use their skills autonomously in their future lives, they will need opportunities to work on less structured problems in their classrooms.

• Concept Development Lessons - "How can I help students develop a deeper understanding of mathematics?" 

Professional development materials created by the Math Assessment Project (MAP) at the Shell Center.  Concept Development lessons are intended to assess and develop students’ understanding of fundamental concepts through activities that engage them in classifying and defining, representing concepts in multiple ways, testing and challenging common misconceptions, and exploring structure.  This PD module, focuses on Concept Development lessons. Research has shown that individual, routine practice on standard problems does little to help students deepen their understanding of mathematical concepts. Teaching becomes more effective when existing interpretations (and misinterpretations) of concepts are shared and systematically explored within the classroom. The lessons described here typically begin with a formative assessment task that exposes students’ existing ways of thinking. The teacher is then offered specific suggestions on how these may be challenged and developed through collaborative activities. New ideas are constructed through reflective discussion. This process places considerable pedagogic demands on teachers, and it is these demands that this module is intended to explore. 

• Improving Learning Through Questioning - "How can we ask questions that improve thinking and reasoning?"
  

 Professional development materials created by the Math Assessment Project (MAP) at the Shell Center.  One important way of moving students’ thinking forward is to prompt them to reconsider their reasoning by asking carefully chosen questions. This unit contains a selection of professional activities that are designed to help teachers to reflect on: 

• characteristics of their questioning that encourage students to reflect, think and reason;
• ways in which teachers might encourage students to provide extended, thoughtful answers, without being afraid of making mistakes;
• the value of showing students what reasoning means by ‘thinking aloud’.

• Students Learning Collaboratively - "How can students learn from discussing mathematics?" 

Professional development materials created by the Math Assessment Project (MAP) at the Shell Center.  If students are to make sense of mathematical concepts, then they will need opportunities to share, discuss and work together. Research has shown that cooperative small group work has positive effects on learning, but that this is dependent on the existence of shared goals for the group and individual accountability for the attainment of these goals. It has also been seen to have a positive effect on social skills and self-esteem (Askew & Wiliam, 1995).  In many classrooms, however, traditional transmission teaching styles have reduced both the quantity and quality of student-student discussion. In others, students do work and talk together, but this talk does not always profit learning. This unit is designed to help teachers to:

• consider the characteristics of student-student discussion that benefit learning;
• recognize and face their own worries about introducing collaborative discussion;
• explore techniques for promoting effective student-student discussion;
• consider their own role in managing student-student discussion; 
• plan discussion based lessons. 

PRIMAS Professional Development Modules

• Professional Development Modules for Inquiry-based, Collaborative Learning 

Part of the PRIMAS (Promoting Inquiry in Mathematics and Science Education Across Europe) project, these modules explore some of the pedagogical challenges that arise when introducing investigative, non-routine problem solving activities to the classroom.  The modules are activity-based; built around a collection of example classroom activities. The intention is that, as part of the Professional Development (PD) process, teachers will plan inquiry-based lessons to use with their own class and, at a later meeting, report back on their experiences.

Math Professional Development Modules from Achieve the Core

• Introduction to the Math Shifts

• Diving Deep into the Math Shifts