HOW DO WORKING ON MATHEMATICALLY CHALLENGING TASKS AND DIFFERENTIATION PLAY OUT IN MODULE 2

Lesson planning is at the heart of successful teaching. Several scholars highlight the role of good planning, by arguing that it determines the resources a teacher can draw upon while trying to be attentive to the subject matter and the students; several scholars also emphasize its contribution to quality teaching (e.g., Lampert, 2001; Nilsson, 2009; Reynolds, 1992). In this respect, selecting, analyzing and modifying challenging tasks during lesson planning sets the ground for engaging all students in mathematically challenging work during teaching. In this context, the purpose of the current module is to help teachers improve their knowledge and skills in selecting and analyzing/modifying challenging mathematics tasks for all their students.

The module consists of three Cases of Practice. Analytically, in Case of Practice 1, entitled “Planning a Lesson: Selecting and Analyzing Mathematically Challenging Tasks”, teachers are first encouraged to consider what makes a task challenging by analyzing it and identifying its level of mathematical challenge as it originally appears in the curriculum materials and as it is enacted during teaching. Next, in Case of Practice 2 (that is, Planning for Differentiation: Considering the Task for Different Students) attention is centered on tasks per se, and teachers are expected to go deeper into identifying what makes a task mathematically challenging for different groups of students; they are also provided with opportunities to discuss how the mathematical challenge of a task can be adjusted to ensure that students are mathematically challenged at an appropriate level. After that, in Case of Practice 3 (i.e, “Planning for Differentiation: Bringing Considerations of my Students Into the Picture”) factors related to students which have been put at the background in Case of Practice 2 are brought to the forefront and teachers are encouraged and supported to consider some tools which will help them in thinking and analyzing student prior knowledge. They are also scaffolded to anticipate possible student alternative conceptions and solutions during the lesson planning phase; doing so is expected to help teachers become more prepared to capitalize on such conceptions and solutions should they arise during the lesson.

Participants of Module 2 are expected to be familiar with the dual goal of engaging all students in mathematically challenging work through the work they will have already done in Module 1. In Module 1, the work around this dual goal was organized around three categories, which correspond to lesson planning, student autonomous work, and whole-class discussion; these three phases are considered as three key parts, where the enactment of mathematically challenging tasks and differentiation can take place. Building on the work that will have been done in the introductory Module 1, participants of Module 2 will delve deeper into issues related to mathematically challenging tasks and differentiation during lesson planning. The remaining modules pertain to the other two phases of the lesson implementation (students’ autonomous work – Module 3; and whole-class discussion – Module 4), and to establishing a culture that fosters mathematical challenge and differentiation (Module 5).

In this respect, selecting, analyzing and modifying challenging tasks during lesson planning sets the ground for engaging all students in mathematically challenging work during teaching. In this context, the purpose of the current module is to help teachers improve their knowledge and skills in selecting and analyzing/modifying challenging mathematics tasks for all their students.

The module consists of three Cases of Practice. Analytically, in Case of Practice 1, entitled “Planning a Lesson: Selecting and Analyzing Mathematically Challenging Tasks”, teachers are first encouraged to consider what makes a task challenging by analyzing it and identifying its level of mathematical challenge as it originally appears in the curriculum materials and as it is enacted during teaching. Next, in Case of Practice 2 (that is, Planning for Differentiation: Considering the Task for Different Students) attention is centered on tasks per se, and teachers are expected to go deeper into identifying what makes a task mathematically challenging for different groups of students; they are also provided with opportunities to discuss how the mathematical challenge of a task can be adjusted to ensure that students are mathematically challenged at an appropriate level. After that, in Case of Practice 3 (i.e, “Planning for Differentiation: Bringing Considerations of my Students Into the Picture”) factors related to students which have been put at the background in Case of Practice 2 are brought to the forefront and teachers are encouraged and supported to consider some tools which will help them in thinking and analyzing student prior knowledge. They are also scaffolded to anticipate possible student alternative conceptions and solutions during the lesson planning phase; doing so is expected to help teachers become more prepared to capitalize on such conceptions and solutions should they arise during the lesson.
Participants of Module 2 are expected to be familiar with the dual goal of engaging all students in mathematically challenging work through the work they will have already done in Module 1. In Module 1, the work around this dual goal was organized around three categories, which correspond to lesson planning, student autonomous work, and whole-class discussion; these three phases are considered as three key parts, where the enactment of mathematically challenging tasks and differentiation can take place. Building on the work that will have been done in the introductory Module 1, participants of Module 2 will delve deeper into issues related to mathematically challenging tasks and differentiation during lesson planning. The remaining modules pertain to the other two phases of the lesson implementation (students’ autonomous work – Module 3; and whole-class discussion – Module 4), and to establishing a culture that fosters mathematical challenge and differentiation (Module 5).

Dear Readers,

On behalf of all the members of the European ERASMUS+ project entitled, “Enhancing Differentiated Instruction and Cognitive Activation in Mathematics Lessons by Supporting Teacher Learning (EDUCATE)”, I would like to welcome you to our project’s educational materials for teacher educators.

Sponsored by the ERASMUS+ programme of the European Union, the transnational project EDUCATE aims at integrating cognitive activation (i.e., working with challenging tasks) and differentiation, aspiring to promote both aspects in the subject of Mathematics, through the provision of appropriate support to teachers and teacher educators. Specifically, we have created these materials with the intention of scaffolding teacher educators in productively supporting teachers in helping all their students work on mathematically challenging tasks.

Partners from four European countries, namely Cyprus, Greece, Ireland, and Portugal have worked closely together to develop, pilot test, and refine these materials, as well as design a professional development process around them. Before producing these materials, a thorough review of the current literature and European/International and national documents in the four participated countries (i.e., top-down approach) was conducted; a needs-assessment analysis to identify prospective and practicing teachers’ needs, challenges, and difficulties as they enact challenging tasks with all their students that cut across different European educational systems was also conducted by observing/analyzing a series of lessons in the four participating countries; reflective post-lesson discussions were also conducted with teachers (i.e., bottom-up approach). Moreover, we have solicitated practicing teachers and school inspectors’ feedback on the clarity of the modules, their reasonableness, applicability and usefulness, in order to improve them.

The project in general, and the production of these materials, in particular, could not have been realized without the support of the teachers who volunteered to participate in the different phases of the project, whom we would like to thank for opening their classrooms and letting us explore their practice and think with them about the complexities inherent in working with challenging tasks with all students.

We would like to invite you to implement these materials with teachers in the context of video-club settings. Should you have any questions about the project or if you have any feedback for its rationale, activities, and publications, please visit our portal http://www.ucy.ac.cy/educate/en/ and explore it to get more information about the progress of the project and its outcomes. You could also directly contact the local coordinators from each partner country:

  • University of Cyprus (Cyprus, Dr. Charalambos Y. Charalambous, cycharal@ucy.ac.cy)
  • National and Kapodistrian University of Athens (Greece, Professor Despina Potari, dpotari@math.uoa.gr)
  • Marino Institute of Education (Ireland, Dr. Seán Delaney, delaney@mie.ie)
  • Universidade de Lisboa (Portugal, Professor João Pedro da Ponte, jpponte@ie.ulisboa.pt)

 

On Behalf of the EDUCATE Project members,

The Project Coordinator,

Dr. Charalambos Y. Charalambous

Assistant Professor of Educational Research and Evaluation

Department of Education, University of Cyprus

Course Curriculum

GENERAL GUIDELINES
GENERAL GUIDELINES Unlimited
INTRODUCTION
TEM2 – ANALYZING TASKS: A KEY ASPECT OF LESSON PLANNING FOR (PRE-)PRIMARY Unlimited
CASE OF PRACTICE 1
TEM2 – CP1 – Planning a Lesson: Selecting and Analyzing Challenging Tasks Unlimited
TEM2 – CP1 – Activity 1 – The Task Analysis Guide Unlimited
TEM2 – CP1 – Activity 2 – Selecting and Analyzing Tasks Using the TAG Unlimited
TEM2 -CP1 – Activity 3 – From Task Selection to Task Presentation and Implementation Unlimited
TEM2 – CP1 – Connections to My Practice Unlimited
TEM2 – CP1 – Closing Activity Unlimited
CASE OF PRACTICE 2
TEM2 – CP2 – Planning for Differentiation: Considering the Task for Different (Groups of) Students Unlimited
TEM2 – CP2 – Activity 1 – Analyzing Practice Unlimited
TEM2 – CP2 – Activity 2 – Considering Factors Influencing Task Implementation Unlimited
TEM2 – CP2 – Activity 3 – Planning for the Use of Enablers and Extenders Unlimited
TEM2 – CP2 – Connections to My Practice Unlimited
TEM2 – CP2 – Closing Activity Unlimited
CASE OF PRACTICE 3
TEM2 – CP3 – Planning for Differentiation: Bringing Considerations of my Students into the Picture Unlimited
TEM2 – CP3 – Activity 1 – Bringing Students Back to the Picture Unlimited
TEM2 – CP3 – Activity 2 – Thinking and Analyzing Student Prior Knowledge Unlimited
TEM2 – CP3 – Activity 3 – Anticipating Student Alternative Conceptions Unlimited
TEM2 – CP3 – Activity 4 – Anticipating Possible Student Solutions Unlimited
TEM2 – CP3 – Closing Activity Unlimited
APPENDIX
Appendix Unlimited

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