Teaching with Tasks for Effective Mathematics Learning

By: Peter Sullivan, Doug Clarke, Barbara Clarke

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Hardcover | 12 September 2012

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Hardcover
222 Pages

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23.39 x 15.6 x 1.42

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âThis book is about how teachers can use classroom mathematics tasks to support student learning, and presents data on the ways in which teachers used those tasks in a particular research project. It is the product of research findings focusing on teacher practice, teacher learning and knowledge, and student learning. It demonstrates how teachers can use mathematics tasks to promote effective student learning.â

Industry Reviews

From the reviews:

"In this book, Sullivan, Clarke and Clarke make an important contribution to the growing literature on mathematics tasks as they outline the findings from their three-year project Task Types in Mathematics Learning ... . This book underlines the value of research-designed and collaboratively-developed mathematics tasks. ... this book will be very widely read, and that the tasks found here, and others like them, will be able to benefit many more students of mathematics." (Colin Foster, Research in Mathematics Education, Vol. 15 (3), 2013)

"The authors discuss a wide variety of classroom mathematical tasks that may enhance the learning of mathematics for students and also make the teaching of mathematics more enjovable. This book also provides some student feedback to certain tasks. The authors study in depth how teachers act when using tasks." (Fiacre O'Cairbre, zbMATH, Vol. 1268, 2013)

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Researching Tasks in Mathematics Classrooms	p. 1
The Tasks Type and Mathematics Learning Project	p. 1
Using This Book	p. 4
Perspectives on Mathematics, Learning, and Teaching	p. 7
The Mathematics It Is Intended that Students Learn	p. 7
Fostering a Breadth of Mathematical Actions	p. 8
Considering Students' Perspectives on Mathematical Tasks	p. 9
Approaches to Teaching Mathematics	p. 10
Summary	p. 12
Tasks and Mathematics Learning	p. 13
Introduction	p. 13
The Connection Between Tasks and Learning	p. 14
Types of Tasks for Mathematics Teaching	p. 15
The Role of Teacher Knowledge in Effective Task Use	p. 15
Teacher Beliefs, Attitudes, and Self-Goals	p. 18
Constraints	p. 19
Teacher Intentions	p. 20
Summary	p. 21
Using Purposeful Representational Tasks	p. 23
A Rationale for Purposeful Representational Tasks	p. 23
Defining Purposeful Representational Tasks in the TTML Project	p. 25
An Example of a Purposeful Representational Task: Colour in Fractions	p. 25
Colour in Fractions	p. 25
Some Additional Examples	p. 28
Sourcing and Creating Purposeful Representational Tasks	p. 29
Some Reactions from Project Teachers to Purposeful Representational Tasks	p. 29
The Teachers' Definitions of the Tasks	p. 29
Some Examples of the Tasks that Teachers Valued	p. 30
The Advantages of Purposeful Representational Tasks as Seen by the Teachers	p. 31
The Constraints on the Use of Purposeful Representational Tasks as Seen by the Teachers	p. 32
The Challenges of Teaching Purposeful Representational Tasks: Learning to Use a Ratio Table	p. 32
Making Cordial: Taking Opportunities	p. 33
Bottles Task: Accepting Different Strategies	p. 33
Medals at the Shrine: Operationalising the Tool	p. 36
Summary	p. 36
Using Mathematical Tasks Arising from Contexts	p. 39
A Rationale for Tasks Built Around Practical Contexts	p. 39
The Contextualised Tasks That Were the Focus of Our Project	p. 42
A Specific Example of a Contextualised Task	p. 43
Setting the Scene	p. 43
Enabling Prompts	p. 43
Students' Strategies	p. 44
Building upon Students' Insights	p. 45
Pulling the Lesson Together	p. 45
Students as Problem Posers	p. 46
Some Examples of Contextualised Tasks Which Teachers Valued	p. 46
Some Reactions from Teachers to Contextualised Tasks	p. 48
Teachers' Views on Advantages and Difficulties in Using Contextualised Tasks	p. 49
Teacher Actions and Their Impact on Task Potential and Student Learning	p. 50
Teacher A	p. 50
Teacher B	p. 52
Teacher C	p. 53
Some Reflections on the Three Lessons	p. 54
Sourcing and Creating Contextualised Tasks	p. 54
Taking Prompts and Using Them to Develop Contextualised Tasks	p. 55
Summary	p. 56
And Where Was the Photograph Taken?	p. 56
Using Content-Specific Open-Ended Tasks	p. 57
The Potential Contribution from Open-Ended Tasks to Student Learning	p. 57
Creating a Learning Experience Around a Content-Specific Open-Ended Task	p. 59
Insights into Related Teacher Actions Based on Observations During the Project	p. 61
Finding Out What the Students Are Actually Doing Is Difficult	p. 62
Sometimes Communicating the Precision of Mathematical Language Is Helpful	p. 63
It Is Important that Questions Are Purposeful	p. 63
There Is No Need to Talk All the Time	p. 64
It Is Useful to Be Aware of Reluctant Contributors	p. 64
Examples of Content-Specific Open-Ended Tasks	p. 64
Some Reactions from Project Teachers to Open-Ended Tasks	p. 65
The Teachers' Definitions of the Tasks	p. 65
Some Examples of the Tasks that Teachers Valued	p. 66
The Advantages of Open-Ended Tasks as Seen by the Teachers	p. 67
The Constraints on the Use of Open-Ended Tasks as Seen by the Teachers	p. 67
Sourcing and Creating Content-Specific Open-Ended Tasks	p. 68
Working Backwards	p. 68
Adapting a Standard Question	p. 69
Summary	p. 70
Moving from the Task to the Lesson: Pedagogical Practices and Other Issues	p. 71
Looking for Three More: An Open-Ended Task to Challenge and Enhance Students' Understanding of (Mean) Average	p. 72
Being Clear on the Mathematical Focus and the Goals of the Lesson for Students	p. 72
Considering the Background Knowledge Which Student Are Likely to Bring to the Task, How to Establish This, and Likely Responses Students Will Make to the Tasks, Including the Difficulties They Might Experience	p. 73
Considering Ways in Which Students Who Have Difficulty Making a Start on the Problem and Students Who Solve the Problem Quickly Might Best Be Supported	p. 74
Monitoring Students' Responses to Tasks as They Work Individually or in Small Groups on the Tasks	p. 74
Selecting Students Who Will Be Invited to Share During the Discussion Time	p. 79
Focusing on Connections, Generalisation, and Transfer	p. 80
Considering What the Next Lesson Might Look Like	p. 81
Differences Between Task Types in Relation to the Process of Turning a Task into a Lesson	p. 82
Summary	p. 83
Constructing a Sequence of Lessons	p. 85
Introduction	p. 85
A Sequence of Lessons on Presenting and Interpreting Data	p. 86
An Investigative Project as an Overarching Theme	p. 87
Most Popular Letter	p. 88
Introducing Graphical Representations	p. 89
Features of Graphical Representations	p. 89
Matching Graphical Representations	p. 89
Conducting and Representing Survey Results	p. 90
Making Decisions on Representations	p. 91
Finding Similar Graphs	p. 91
Rock, Paper, Scissors	p. 92
Two-Way Tables	p. 92
Average Height of Class	p. 93
Mean Average	p. 94
A Sentence with Five Words	p. 94
Average Height of the School	p. 95
Comparing and Contrasting Measures of Centre and Spread	p. 95
Seven People Went Fishing	p. 95
Clues on Cards	p. 96
Post-sequence Assessment and Evaluation	p. 96
The Lesson Observations, Including Observations of Lesson Five	p. 97
Summary	p. 98
Students' Preferences for Different Types of Mathematics Tasks	p. 99
Seeking Students' Opinions About Tasks	p. 99
Responses of Students to Pre-determined Prompts About Tasks and Pedagogies	p. 100
Students' Attitudes	p. 101
In Summary	p. 106
Tasks Preferences Within a Lesson Sequence	p. 107
Summary	p. 109
Students' Perceptions of Characteristics of Desired Mathematics Lessons	p. 111
Responses from the Overall Survey on Desired Lesson Characteristics	p. 111
Students' Essays on Their "Ideal Maths Class"	p. 115
Some Themes in the Data	p. 117
Classroom Grouping	p. 117
Interaction Between Teacher and Students	p. 119
Summary	p. 120
Contrasting Types of Tasks: A Story of Three Lessons	p. 121
The Tasks and the Lessons	p. 122
Inside and Outside the Square	p. 122
Dido's Problem	p. 122
What the L?	p. 123
Results: Teacher Data	p. 126
Order of Teaching	p. 126
Teaching and Learning Challenges	p. 127
Teacher Preferences	p. 128
One Teacher's Contrast Between Types of Tasks	p. 130
Student Responses	p. 131
Student Preferences	p. 131
Advice on Improving Lessons	p. 132
Summary Comments from the Student Data	p. 133
Relationship Between the Student Preferences and the Teacher Preferences	p. 133
Summary	p. 134
Conclusion	p. 135
What We Learnt About the Different Types of Tasks	p. 136
Purposeful Representational Tasks	p. 136
Contextual Tasks	p. 137
Open-Ended Tasks	p. 137
Other Types of Tasks	p. 138
Planning for Task Implementation (or Turning the Task into a Lesson)	p. 138
Differences in Task Implementation	p. 139
Opportunities and Constraints in Task Use	p. 141
Students and Mathematics Tasks	p. 143
A Selection of Mathematical Tasks	p. 145
Purposeful Representational Tasks	p. 146
Chocholate Blocks	p. 147
Clues on Cards	p. 149
Decimal Maze	p. 152
Smartie Predictions	p. 155
Matching Graphical Representations	p. 159
Five Contextualised Tasks	p. 161
Music Cards	p. 162
Mike and His Numbers	p. 165
Block of Land	p. 168
Comparing Coins from Different Countries	p. 173
Content-Specific Open-Ended Tasks	p. 176
Wrap the Present	p. 177
Painting a Room	p. 180
Writing a Sentence	p. 183
Different Ways to Represent Data	p. 186
Money Measurement	p. 190
References	p. 195
Index	p. 201
Table of Contents provided by Ingram. All Rights Reserved.

Teaching with Tasks for Effective Mathematics Learning

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

Other Books By Peter Sullivan

Challenging Mathematical Tasks

Unlocking the potential of all students

Open Ended Maths Activities

Revised Edition - Using good questions to enhance learning mathematics

Maths Sequences for the Early Years F-2

Challenging Children to Reason Mathematically

Building Engagement in Middle Years Mathematics

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Nutrition and Neurodisability

Mac Keith Press Practical Guides

Constructing Knowledge for Teaching Secondary Mathematics

Tasks to enhance prospective and practicing teacher learning

Wittgenstein's Tractatus

History and Interpretation