Logo is one of the most powerful settings for teaching and learning geometry and algebra. Many publications support this stance and two excellent examples follow:

These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.Essays in the first section discuss the link between Logo and the school mathematics curriculum, focusing on the ways in which pupils' Logo activities relate to and are influenced by the ideas they encounter in the context of school algebra and geometry.In the second section the contributions take up pedagogical styles and strategies. They tackle such cognitive and metacognitive questions as, What range of learning styles can the Logo setting accommodate? How can teachers make sense of pupils' preferred strategies? And how can teachers help students to reflect on the strategies they are using?Returning to the mathematical structures, essays in the third section consider a variety of mathematical ideas, drawing connections between mathematics and computing and showing the ways in which constructing Logo programs helps or does not help to illuminate the underlying mathematics.Celia Hoyles; is Professor of Mathematics Education at the Institute of Education, University of London, where Richard Noss is Chair of the Department of Mathematics, Statistics, and Computing. Logo and Geometry, JRME Monograph #10 written by Douglas Clements, Michael Battista, Julie Sarama, and Erna Yackel.

Funded by the National Science Foundation, the purpose of the LOGO Geometry Project was to develop a research-based grades K–6 geometry curriculum that addressed the deficits of the current curriculum. In addition to introducing the project and its rationale, this monograph details the research, results, and implications of the study.

Logo has a rich and fascinating history. Two excepts from The National Logo Exchange January 1986 newsletter follow.

From the NLXtra supplement, I found information on a Logo Tour. The International Logo Exchange (ILX) announces its 1986 Iceland & Netherlands Logo Tour. Led by ILX editor Dennis Harper, the 14-day tour will include Logo workshops, presentations, school site visits, lectures, dinners with host country Logo educators, and many other exciting Logo activities. Logo educators at all levels are invited to participate in this international Logo event. The tour will visit both Iceland and the Netherlands, spending approximately one week in each country. All tour participants will deliver one workshop or paper to Icelandic or Dutch colleagues. The tour departs New York on August 11, 1986, and returns on August 25. (Departures from other cities can be arranged easily.) The $1589 price encompasses all air fares, transfers, tours, hotels, 2 meals per day, and all educational activities, including three quarter units of graduate credit through the University of California.

Is there competition? Yes.

Logo publications primarily focus on coding (algorithmic thinking, computational thinking) and learning the commands (syntax).
The Terrapin Logo Bibliography page lists numerous book titles on learning programming and completing projects.

GoLogo by Marla Weiss covers 100 commands and numerous skills that are good to know, but are not necessary if mathematics is the primary focus. The chapter structure shown below follows a programming approach.

Go, Logo utilizes Logo programming to teach math concepts in a hands on way to help students master them. It is targeted at middle school students but is also appropriate for advanced math upper elementary students and for math reinforcement for high school students. Concepts 1: Zero Heading and Marking Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 2: Total Turtle Trip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 3: Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 4: Local Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 5: Numbers, Words, and Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 6: Top-Down Design and Debugging Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 7: Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 8: Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 9: Arrays and Multiple Turtles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 10: Concatenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concepts 11: Accumulator, Counter, and Flag Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . A companion Go, Logo Solutions contains answers to all the problems for the instructor. Logo Works: Lessons in Logo by Sheila Cory and Margie Walker. A sample chapter is shown here. Chapter Five – Circles ....................................................................113 LESSON 1 Approximating a Circle...................................................113 LESSON 2 Changing the Size of a Circle........................................116 LESSON 3 Diameter and Radius ....................................................120 LESSON 4 Another Look at Circles .................................................123 LESSON 5 Designs With Circles .....................................................126 LESSON 6 180 Degree Arcs ...........................................................129 LESSON 7 90 Degree Arcs .............................................................132 LESSON 8 Putting it all Together!....................................................135
The texts written by Meiyu Fu looks quite promising but they are written in Chinese.

Fu, Meiyu

Logo Technology and Middle School Mathematics

Guizhou Education Publishing

2007

Chinese

Fu, Meiyu and Fu, Yuaning

Logo Mathematics Laboratory

Publishing House of Electronics Industry

2002

Chinese

Some books address the need to teach coding / computational thinking, but don't include much mathematics. For example, I received an email promoting No Fear Coding: Computational Thinking Across the K-5 Curriculum (2017)written by Heidi Williams. The table of contents indicates that the Heidi is making a case about why to teach coding and what instruction would look like (How to Teach ...). Learning mathematics does not appear to be front and center in this type of text. H

TABLE OF CONTENTS Introduction: The Industrial Model of Education Must Change ..................1

Part 1: Coding and Computational Thinking.....................................6 CHAPTER 1: Why Should K–5 Educators Teach Coding?..........................8 CHAPTER 2: Coding = Computational Thinking .....................................16 CHAPTER 3: How Does Coding Fit into Curriculum?..............................22 CHAPTER 4: What Teaching Coding Looks Like......................................31

Part 2: Engaging Young Coders with Bee-Bots...............................42 CHAPTER 5: Why Teach with Bee-Bots?...................................................44 CHAPTER 6: How to Teach with Bee-Bots................................................49 CHAPTER 7: Bee-Bots in the Classroom—Case Studies...........................60

Part 3: Introduce Coding with Code.org ..........................................64 CHAPTER 8: Why Introduce Students to Coding with Code.org?.........66 CHAPTER 9: How to Use Code.org within the Curriculum.....................69 CHAPTER 10: Code.org in the Classroom—Case Studies........................85

Part 4: Incorporate Scratch Across the Curriculum.........................92 CHAPTER 11: Why Teach Coding and Computational Thinking with Scratch? .......................................................94 CHAPTER 12: How to Teach Using Scratch...............................................99 CHAPTER 13: Scratch Projects Across the Curriculum .........................107 Part 5: Coding and Beyond .................................................................120 CHAPTER 14: Create Real-World Experiences with ARIS .....................122

Conclusion ...............................................................................................130 References ...............................................................................................133 Appendix A: ISTE Standards for Students ..............................................138 Appendix B: Standards for Mathematical Practice.................................142

## Why publish Logo-Math Geometry Lessons?

Logo is one of the most powerful settings for teaching and learning geometry and algebra. Many publications support this stance and two excellent examples follow:

. The book, edited by Hoyles and Noss, is now out of print.Learning Mathematics and Logo (1992)These original essays summarize a decade of fruitful research and curriculum development using the LISP-derived language Logo. They discuss a range of issues in the areas of curriculum, learning, and mathematics, illustrating the ways in which Logo continues to provide a rich learning environment, one that allows pupil autonomy within challenging mathematical settings.Essays in the first section discuss the link between Logo and the school mathematics curriculum, focusing on the ways in which pupils' Logo activities relate to and are influenced by the ideas they encounter in the context of school algebra and geometry.In the second section the contributions take up pedagogical styles and strategies. They tackle such cognitive and metacognitive questions as, What range of learning styles can the Logo setting accommodate? How can teachers make sense of pupils' preferred strategies? And how can teachers help students to reflect on the strategies they are using?Returning to the mathematical structures, essays in the third section consider a variety of mathematical ideas, drawing connections between mathematics and computing and showing the ways in which constructing Logo programs helps or does not help to illuminate the underlying mathematics.Celia Hoyles; is Professor of Mathematics Education at the Institute of Education, University of London, where Richard Noss is Chair of the Department of Mathematics, Statistics, and Computing.Logo and Geometry, JRME Monograph #10 written by Douglas Clements, Michael Battista, Julie Sarama, and Erna Yackel.

Funded by the National Science Foundation, the purpose of the LOGO Geometry Project was to develop a research-based grades K–6 geometry curriculum that addressed the deficits of the current curriculum. In addition to introducing the project and its rationale, this monograph details the research, results, and implications of the study.Logo has a rich and fascinating history. Two excepts from The National Logo Exchange January 1986 newsletter follow.

From the NLXtra supplement, I found information on a Logo Tour.

The International Logo Exchange (ILX) announces its 1986 Iceland & Netherlands Logo Tour. Led by ILX editor Dennis Harper, the 14-day tour will include Logo workshops, presentations, school site visits, lectures, dinners with host country Logo educators, and many other exciting Logo activities. Logo educators at all levels are invited to participate in this international Logo event. The tour will visit both Iceland and the Netherlands, spending approximately one week in each country. All tour participants will deliver one workshop or paper to Icelandic or Dutch colleagues. The tour departs New York on August 11, 1986, and returns on August 25. (Departures from other cities can be arranged easily.) The $1589 price encompasses all air fares, transfers, tours, hotels, 2 meals per day, and all educational activities, including three quarter units of graduate credit through the University of California.## Is there competition? Yes.

Logo publications primarily focus on coding (algorithmic thinking, computational thinking) and learning the commands (syntax).The Terrapin Logo Bibliography page lists numerous book titles on learning programming and completing projects.

GoLogo by Marla Weiss covers 100 commands and numerous skills that are good to know, but are not necessary if mathematics is the primary focus. The chapter structure shown below follows a programming approach.

Go, Logo utilizes Logo programming to teach math concepts in a hands on way to help students master them. It is targeted at middle school students but is also appropriate for advanced math upper elementary students and for math reinforcement for high school students.Concepts 1: Zero Heading and Marking Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 2: Total Turtle Trip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 3: Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 4: Local Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 5: Numbers, Words, and Lists . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 6: Top-Down Design and Debugging Tips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 7: Global Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 8: Stacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 9: Arrays and Multiple Turtles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 10: Concatenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Concepts 11: Accumulator, Counter, and Flag Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . .A companionGo, Logo Solutionscontains answers to all the problems for the instructor.Logo Works: Lessons in Logo by Sheila Cory and Margie Walker. A sample chapter is shown here.

Chapter Five – Circles ....................................................................113LESSON 1 Approximating a Circle...................................................113LESSON 2 Changing the Size of a Circle........................................116LESSON 3 Diameter and Radius ....................................................120LESSON 4 Another Look at Circles .................................................123LESSON 5 Designs With Circles .....................................................126LESSON 6 180 Degree Arcs ...........................................................129LESSON 7 90 Degree Arcs .............................................................132LESSON 8 Putting it all Together!....................................................135The texts written by Meiyu Fu looks quite promising but they are written in Chinese.

Some books address the need to teach coding / computational thinking, but don't include much mathematics. For example, I received an email promoting No Fear Coding: Computational Thinking Across the K-5 Curriculum (2017)written by Heidi Williams. The table of contents indicates that the Heidi is making a case about why to teach coding and what instruction would look like (How to Teach ...). Learning mathematics does not appear to be front and center in this type of text. H

TABLE OF CONTENTS

Introduction: The Industrial Model of Education Must Change ..................1Part 1: Coding and Computational Thinking.....................................6CHAPTER 1: Why Should K–5 Educators Teach Coding?..........................8CHAPTER 2: Coding = Computational Thinking .....................................16CHAPTER 3: How Does Coding Fit into Curriculum?..............................22CHAPTER 4: What Teaching Coding Looks Like......................................31Part 2: Engaging Young Coders with Bee-Bots...............................42CHAPTER 5: Why Teach with Bee-Bots?...................................................44CHAPTER 6: How to Teach with Bee-Bots................................................49CHAPTER 7: Bee-Bots in the Classroom—Case Studies...........................60Part 3: Introduce Coding with Code.org ..........................................64CHAPTER 8: Why Introduce Students to Coding with Code.org?.........66CHAPTER 9: How to Use Code.org within the Curriculum.....................69CHAPTER 10: Code.org in the Classroom—Case Studies........................85Part 4: Incorporate Scratch Across the Curriculum.........................92CHAPTER 11: Why Teach Coding and ComputationalThinking with Scratch? .......................................................94CHAPTER 12: How to Teach Using Scratch...............................................99CHAPTER 13: Scratch Projects Across the Curriculum .........................107Part 5: Coding and Beyond .................................................................120CHAPTER 14: Create Real-World Experiences with ARIS .....................122Conclusion ...............................................................................................130References ...............................................................................................133Appendix A: ISTE Standards for Students ..............................................138Appendix B: Standards for Mathematical Practice.................................142## What is your Philosophy?

(fit to Heinemann)