This page showcases some of the published work of our broader EDC team in mathematics and computer science education.

Found 21 Results

This article addresses the issue of designing a formal curriculum that helps children develop the mathematical habits of mind of creative tinkering, puzzling through, and perseverance.

Goldenberg, E. P. (2019). Problem posing and creativity in elementary-school mathematics.* Constructivist Foundations, 14*3(3), 319–341.

This paper shows how children use mathematical “maker spaces,” microworlds, which are inspired and informed by the way children, especially young children, use linguistic pattern in spoken language to build mathematical ideas and explains how programming can be a valuable third language for mathematics, supporting creative exploration, key content, and essential mathematical habits of mind. Computer science and computational thinking develops in tandem, integrated into the mathematical thinking.

Goldenberg, E. P., & Carter, C. (in press). How programming can serve young children as a language from expressing and exploring mathematics in their classes. *Constructionism 2020.*

In this blog post, EDC’s Paul Goldenberg, June Mark, Deborah Spencer, Kate Coleman, and Kristen Reed investigate whether computer programming can help young children with mathematics.

Granofsky, B. (2019, December 10). A new language for mathematics. Education Development Center. Retrieved from https://www.edc.org/new-language-mathematics

In episode 32 of EDC’s podcast, *Mosaic*, Paul Goldenberg and Kristen Reed discuss why they think programming is an effective tool for expressing mathematical ideas and share stories from investigating this in the classroom.

Education Development Center. (Producer). (2020, April 23). *Could computer programming help children learn math? *[Audio podcast]. https://soundcloud.com/education-development-center/ep-32-could-computer-programming-help-children-learn-math

In this episode of the podcast, *Kids Lab*, hosted by Sven Haiges, Kristen Reed and Paul Goldenberg discuss their investigation into whether learning computer programming can help young children learn mathematics.

KidsLab. (Producer). (2020, June 8). *Learning Math via Computer Programming with Kristen Reed and Paul Goldenberg *[Audio podcast]. https://kidslab.dev/2020/06/08/learning-math-via-computer-programming-with-kristen-reed-and-paul-goldenberg/

In this article, Paul Goldenberg discusses what’s useful about creating a puzzle or posing a problem and how might puzzles and problem posing support mathematical learning.

Goldenberg, E. P. (2018). Teaching children to be problem posers and puzzle creators in mathematics. In V. Dagiené & E. Jasuté (Eds.).* Constructionism 2018, Vilnius Conference Proceedings *(pp. 39–52)*. *Retrieved from http://www.constructionism2018.fsf.vu.lt/file/repository/Proceeding_2018_Constructionism.pdf

This book, published by the National Council of Teachers of Mathematics (NCTM), focuses on essential knowledge for teachers about geometry and measurement in the early elementary grades. Organized around four big ideas, and supported by multiple smaller, interconnected ideas—*essential understandings*—teachers will learn how to engage their students by anticipating their perplexities, avoiding pitfalls, and dispelling misconceptions while learning to develop appropriate tasks, techniques, and tools for assessing students’ understanding of the topic.

Goldenberg, E. P., & Clements, D. (2014). *Developing essential understanding of geometry and measurement for teaching mathematics in pre-K–2*. Reston, VA: National Council of Teachers of Mathematics.

This article, published in *NCTM’s Teaching Children Mathematics*, discusses why taking advantage of the natural logic and algebraic ideas of young learners will produce students who are better prepared for arithmetic as well as algebra in the later grades.

Goldenberg, E. P., Mark, J., & Cuoco, A. (2010). An algebraic habits-of-mind perspective on elementary school. *Teaching Children Mathematics, (16)*9, 548–556.

In this blog post, EDC’s Paul Goldenberg shares his belief that computer programming belongs in K–5 classrooms—and that it’s not about turning every child into a computer scientist.

Goldenberg, E. P. (2017, April 10). Should all children learn to code [Blog post]. Retrieved from https://www.edc.org/should-all-children-learn-code

In this blog post, EDC’s Paul Goldenberg, Kristen Reed, and Jessica Young share some fun and easy games to play with your preschooler or kindergartener.

Goldenberg, E. P. (2016, September 28). 5 math games to inspire young minds [Blog post]. Retrieved from https://www.edc.org/5-math-games-inspire-young-minds

In this video, NSF-funded researchers Arthur Barody, Jere Confrey, Julie Sarama, and EDC’s Paul Goldenberg discuss the importance of mathematics education in the early grades.

CADREK12. (2018, September 24). *The importance of early math education* [Video]. YouTube. https://www.youtube.com/watch?v=W2b6TXJsY4Y&feature=youtu.be

In this blog post (which includes a video), EDC’s Kristen Reed shares some fun and easy math activities to do at home with your early childhood and elementary-aged children.

Reed, K. (2019, December 4). Making time for family math [Blog post]. Retrieved from https://www.edc.org/edc-talks-making-time-family-math

In the On Teaching and Learning Mathematics blog hosted by the American Mathematical Society, EDC’s Paul Goldenberg shares his thoughts on why trying to figure out what young learners know through listening, observing, and questioning sends a valuable message to them.

Goldenberg, P. (2018, September 2). Ideas under construction: Children saying what they know [Blog post]. Retrieved from https://blogs.ams.org/matheducation/2018/09/02/ideas-under-construction-children-saying-what-they-know/

In the On Teaching and Learning Mathematics blog hosted by the American Mathematical Society, EDC’s Paul Goldenberg and Al Cuoco discuss how pre-service mathematics for elementary (and secondary) teachers must not only include an understanding of fundamental results and methods—content specified in state standards–but also the aspect of mathematics that involves research, play, experimentation, sense making and reasoning.

Goldenberg, P., & Cuoco, A. (2019, September 16). Pre-service mathematics for elementary (and secondary) teachers: A third essential element [Blog post]. Retrieved from https://blogs.ams.org/matheducation/2019/09/16/pre-service-mathematics-for-elementary-and-secondary-teachers-a-third-essential-element/

This collection of six essays shares insights and strategies from EDC’s work to close opportunity gaps in mathematics education and support teachers in improving instruction.

Arthur, C., Badertscher, E., Goldenberg, P., Moeller, B., McLeod, M., Nikula, J., & Reed, K. (2017). *Strategies to improve all students’ mathematics learning and achievement. *Education Development Center: Waltham, MA.

In this blog post, EDC’s Paul Goldenberg makes the case that all students can and should engage in computer science opportunities, not just one week of the year, but every week of the year.

Goldenberg, P. (2019, December 9). Celebrating computer science education week [Blog post]. Retrieved from https://www.edc.org/blog/celebrating-computer-science-education-week

In this blog post, EDC’s Paul Goldenberg, Jessica Young, and Kristen Reed share ways in which all parents and teachers can build “mastery motivation”—the willingness to struggle through tough problems—with their preschoolers.

Goldenberg, P., Young, J., & Reed, K. (2017, July 25). 5 ways to help preschoolers persist in mathematics [Blog post]. Retrieved from https://www.edc.org/5-ways-help-preschoolers-persist-mathematics

*Transition to Algebra*, published by Heinemann, is a full-year curriculum designed by EDC to run concurrently with first-year algebra to raise the competence and confidence of students who may benefit from supports for algebra success. *Transition to Algebra* builds students’ algebraic habits of mind, which are several key mathematical ways of thinking aligned with the Common Core Standards for Mathematical Practice.

Mark, J., Goldenberg, E. P., Fries, M., Kang, J., & Cordner, T. *Transition to Algebra*. Portsmouth, NH: Heinemann.

This book, published by Heinemann, supports grades 6–10 teachers in implementing EDC’s *Transition to Algebra* curriculum. It uses a “habits of mind” approach that helps teachers learn how to teach—not just the results of mathematical thinking, but also the ways of thinking that mathematically proficient individuals use to generate those results.

Goldenberg, E. P., Mark, J., Kang., J., Fries., M., Carter, C., & Cordner, T. (2015). *Making sense of algebra: Developing students’ mathematical habits of mind.* Portsmouth, NH: Heinemann.

This website helps educators understand the role that the Common Core Standards for Mathematical Practice (SMP) play within the larger context of the Common Core Standards themselves. The website uses a series of annotated illustrations, centered on student dialogues, to show the SMP in action. The website also contains information about related professional development initiatives conducted by EDC.

Education Development Center. (2012–2016). Implementing the Mathematical Practice Standards (Website). http://mathpractices.edc.org/