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Children's mathematics 4-15: learning from errors and misconceptions: Learning from Errors and Misconceptions

Children's Mathematics 4-15: Learning from Errors and Misconceptions

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Children's mathematics 4-15: learning from errors and misconceptions: Learning from Errors and Misconceptions

Children's Mathematics 4-15: Learning from Errors and Misconceptions

4.85 47,417 ratings · 7,774 reviews
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Overview: The mistakes children make in mathematics are usually not just 'mistakes' - they are often intelligent generalizations from previous learning. Following several decades of academic study of such mistakes, the phrase 'errors and misconceptions' has recently entered the vocabulary of mathematics teacher education and has become prominent in the curriculum for initial teacher education. The popular view of children's errors and misconceptions is that they should be corrected as soon as possible. The authors contest this, perceiving them as potential windows into children's mathematics. Errors may diagnose significant ways of thinking and stages in learning that highlight important opportunities for new learning.This book uses extensive, original data from the authors' own research on children's performance, errors and misconceptions across the mathematics curriculum. It progressively develops concepts for teachers to use in organizing their understanding and knowledge of children's mathematics, offers practical guidance for classroom teaching and concludes with theoretical accounts of learning and teaching."Children's Mathematics 4-15" is a groundbreaking book, which transforms research on diagnostic errors into knowledge for teaching, teacher education and research on teaching. It is essential reading for teachers, students on undergraduate teacher training courses and graduate and PGCE mathematics teacher trainees, as well as teacher educators and researchers.

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Book details & editions

ISBN
892226
Publication date
November 1, 2006
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Julie Ryan
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Julie Ryan is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Julie Ryan can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Robert Perez
Robert Perez May 15, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Joshua King
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A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Andrew King
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Kevin Martin
Kevin Martin January 29, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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James Jackson January 25, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Anthony King February 28, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Nancy Rodriguez
Nancy Rodriguez August 19, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Steven Hill
Steven Hill June 27, 2024
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
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Carol Martin May 22, 2024
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Christopher Hall
Christopher Hall December 16, 2025
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Ashley Harris November 19, 2024
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Ashley Rodriguez March 16, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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William Brown August 01, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Jacob Adams
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Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
William King
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Andrew Mitchell
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Charles Thompson
Charles Thompson January 04, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Christopher Edwards November 05, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Patricia Sanchez March 02, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Joseph Evans
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Laura Reyes January 01, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Matthew Green
Matthew Green June 17, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Barbara Brown
Barbara Brown June 21, 2025
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Sharon Allen September 24, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Charles Gonzalez
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Steven Sanchez July 17, 2024
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Christopher Martin
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A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Jessica Hall
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I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Matthew Gomez
Matthew Gomez May 27, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Cynthia Johnson
Cynthia Johnson January 26, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Patricia Sanchez April 01, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Daniel Reyes
Daniel Reyes December 27, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Mark Phillips
Mark Phillips May 07, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Andrew Miller
Andrew Miller January 31, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Lisa Taylor
Lisa Taylor August 11, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Richard Allen
Richard Allen April 24, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Richard Carter
Richard Carter June 24, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Karen Flores
Karen Flores September 09, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Andrew Miller
Andrew Miller September 12, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Cynthia Johnson
Cynthia Johnson March 16, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Andrew Roberts
Andrew Roberts August 14, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Edward Sanchez
Edward Sanchez February 08, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Ashley Rodriguez
Ashley Rodriguez November 29, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Jennifer Clark
Jennifer Clark December 22, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Betty Sanchez
Betty Sanchez June 15, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Robert Perez
Robert Perez March 22, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Carol Young
Carol Young May 05, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Karen Martinez
Karen Martinez April 27, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Nancy Adams
Nancy Adams June 17, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
John Carter
John Carter November 19, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Andrew Mitchell
Andrew Mitchell February 24, 2024
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Michael Martin
Michael Martin March 25, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Donna Martin
Donna Martin August 06, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Andrew Roberts
Andrew Roberts April 14, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Eric Edwards
Eric Edwards May 12, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Michael Brown
Michael Brown October 19, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Eric Rivera
Eric Rivera June 15, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
John Thomas
John Thomas September 11, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
William Jones
William Jones March 25, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Robert Lewis
Robert Lewis April 20, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Christopher Jones
Christopher Jones September 10, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Margaret Rivera
Margaret Rivera October 17, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Sarah Brown
Sarah Brown January 02, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Sarah Flores
Sarah Flores June 17, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Andrew King
Andrew King December 04, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Gary Nelson
Gary Nelson January 22, 2025
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Richard Green
Richard Green March 22, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Kenneth Miller
Kenneth Miller December 05, 2024
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Stephanie Evans
Stephanie Evans September 25, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Carol Garcia
Carol Garcia January 16, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
George Cruz
George Cruz June 24, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Ryan Evans
Ryan Evans January 25, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Melissa Allen
Melissa Allen March 09, 2025
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.