Supratimas

Viduramžiais dalyko supratimas reiškė gebėjimą jį mokyti. (Pagal Walter J. Ong. Ramus, Method and the Decay of Dialogue. 1985)   

Šiuolaikinis neuromokslas teigia, kad dalyko supratimas yra ryšių su ankstesniu žinojimu mezgimas. (Pagal L.B. Resnick. Mathematics and science learning: A new conception. Science 1983)

Šiame puslapyje yra nuorodos į tekstus, kuriuose siekiama paaiškinti faktus, procedūras ir teiginius remiantis elementariosios matematikos pagrindinėmis idėjomis

Samprotavimas ir matematika

• • Roger Antonesn. Math is the hidden secret to understanding the world. TEDxOslo. Antonsen explains how a slight change in perspective can reveal patterns, numbers and formulas as the gateways to empathy and understanding.
  • Jelena Mardachajeva. Не пора ли менять школьную математику?     Vesti Obrazovanija, 2019-12-23

Daugyba 

• J. Tanton. The Unreasonableness of K-12 Mathematics.  May 28, 2018.  
• Why Was 5 x 3 = 5 + 5 + 5 Marked Wrong. Science, September 15, 2017.
• Keith Devlin. It’s Still Not Repeated Addition. 2008
• If multiplication is not repeated addition. math.stackexchange.com
• Is it advisable to avoid teaching “multiplication as repeated addition”?  matheducators.stackexchange.com
• Multiplication and repeated addition. Wikipedia
• J. Crabtree. THE LOST LOGIC OF ELEMENTARY MATHEMATICS AND THE HABERDASHER WHO KIDNAPPED KAIZEN.  2016 MAV Anual Conference Proceedings
•  J. Crabtree. Multiplication =/ (not equal) Repeated Addition. Blogg The lost logic of elementary mathematics.
• B. Berry. The “ Zero Power Rule” Explained. Feb 19, 2016.

Dalybos algoritmas

• R. Chawla. Let’s T.I.N.K.E.R. DIVISION !!! Dec 1. 2017.
• L.H. Rogers. In defense of long division: Pro-reform professor capably shows why reform math doesn’t work. Betrayed, 2012.
• M. Goldenberg. What’s Hiding Within Long Division? 2017
• Matt Coaty Using Multiple Strategies in Math Class 

Trupmenos

• E. Gallaher. Mixed Numbers: An Educator’s Guide. Mathspace blog, 2018 mar 27. In many countries mixed numbers are introduced in middle primary. But why? And what use are they?
• Kristin. Fraction Division and Complex Fractions. MathMinds, N0vember 27, 2017.
• L. Bejarano. Two Kinds of Simplicity. Crazy Mathe Teacher Lady, November 24, 2017.
• R.S. Siegler. Fractions: Where It All Goes Wrong. Scientific American, November 28, 2017.
• J. Tanton. Ambiguity and Nuance — Even in Mathematics. Beagle Blog, Nov 26, 2017.
• D. Ludden. Why Is Doing Arithmetic With Fractions So Difficult? Psychology Today, Sept 30, 2017.
• R.S. Siegler, H. Lortie-Forgues. Hard Lessons: Why Rational Number Arithmetic Is So Difficult for So Many People. Current Directions in Psychological Science, 26(4), 346-351, 2017.
• Improving At-Risk Learners’ Understanding of Fractions. American Psychological Association, 2013.

Geometrija

• J. Tanton. Five Objections to teaching the Area Model in Schools. Video

Kas yra sąvokinis supratimas (conceptual understanding)?

• J. Hiebert and T.P. Carpenter.  Learning and teaching with understanding. In  D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (p. 65–97), 1992.
• J.D. Godino. Mathematical concepts. their meanin, and understanding. In L. Puig y A. Gutierrez (Eds.), Proceedings of XX Conference of the International Group for the Psychology of Mathematics Education. (v.2, pp. 417-425), 1996,
• Conceptual Understanding vs. Procedural Fluency. Mind research institute.
• Building conceptual understanding. Mind research institute. Podcast (creating a map instead of giving directions)
• Teaching Mathematics for Understanding.
• Jo Boaler et al. Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning. Journal of Applied and Computational Mathematics, 2016.
• The potential of virtual manipulatives indeveloping mathematical conceptual understanding in primary aged students.
• Ch. Rakes. Challenging the status quo in mathematics: Teaching for understanding. The Conversation, 2017, June 21.
• R.R. Skemp. Relational Understanding and Instrumental Understanding. Mathematics Teaching, 1976, 77, 20-26.
• C. Bell. How to Break the Habit of Teaching Only Procedural Mathematics.
• A.H. Schoenfeld. LEARNING TO THINK M ATHEMATICALLY : PROBLEM SOLVING , METACOGNITION , AND SENSE – MAKING IN M ATHEM ATICS. 1992.
• R. Wegerif. Mind Expanding: Teaching for Thinking and Creativity in Primary Education. 2010
• B. Maj et al (EDS.) Supporting Independent Thinking Through Mathematical Education. Poland, 2008.
• K. Porteous. Understanding Mathematics. Philosophy of Mathematics Education Journal No 23, 2008.
• B. Sriraman, B. Kaiser. Theory usage and theoretical trends in Europe: A survey and preliminary analysis of CERME4 research reports. Survey of working groups. 2006.
• Working Group 3. Building structures in mathematical knowledge. 2005. CERME-4 Proceedings, about 100 pp.
• A. Sierpinska. Some Remarks on Understanding in Mathematics. 1990.

• R.R. Skemp. Relational understanding and instrumental understanding. Mathematics Teaching, 1976.
• M. Chub. Focus on Relational Understanding. July 31, 2016.
• M. Chub. Paying Attention to OUR Understanding!. June 24, 2016.
• Z. Usiskin. What does it mean to understand some mathematics?. 12th International Congress on Mathematical Education, 8 July–15 July, 2012, COEX, Seoul, Korea.

TRU Math (Teaching for robust understanding of mathematics)

• A.H. Schoenfeld. Classroom observations in theory and practice. ZDM Mathematics Education, 2013.
• Teaching for Robust Understanding (TRU). Mathematics Assessment Project.
• Alan Schoenfeld: At the Boundaries of Effective Mathematics Thinking, Teaching, and Learning. Interview. 2017-07-22.
• Hejny method. An approach to mathematics teaching and child development.
• MASS. Project: Motivate and Attract Students to Science, Hejny metod. (Mūsų kaimynai dalyvauja šiame projekte.
• Milan Hejny et al. Understanding equations in schema-oriented education . Procedia, 2013.

Mokymo(si) metodai

• J. Mubeen. How to make every student a maths ‘expert’. Just give them the right problem. Feb. 18, 2018.

Ikimokyklinė matematika

• J.S. McCray. What is Early Math and Why Should We Care? AMS Blogs: On Teaching and Learning Mathematics, November 10, 2015.

Pradinė mokykla

• S. Abaziou.  Encouraging Persistence in MathEdutopia, 24 May, 2018.
• Manipulative mathematics.Manipulatives give students concrete models of abstract mathematical concepts. Students using manipulatives develop conceptual understanding of arithmetic and algebraic topics and procedures because they see how and why the mathematical procedures work.

Pagrindinė mokykla

• Beautiful moments in the HS math curriculum (part 1 of n). Q.E.D.
• D. Siemon, M. Breed, J. Virgona. F ROM ADDITIVE TO MULTIPLICATIVE THINKING – T HE BIG CHALLENGE OF THE MIDDLE YEARS.

Uždaviniai

• Inside mathematics A professional resource for educators.

Egzaminai

• Fisher-Hoch, S. Hughes.   WHAT MAKES MATHEMATICS EXAM QUESTIONS DIFFICULT? 1996.
• PISA test questions.
• Creating Exams.
• Mathematical Lateral Logic Test.

Matematikos vadovėliai

• Suomių vadovėlis Ma.fi

Matematinio ugdymo programos

• Match fishtank
• Center for Curriculum Redesign
• Review of the Australian Curriculum : A statement by the Australian Curriculum, Assessment and Reporting Authority
• M. Oldridge. The Burn It Down and Start Again Mathematics Curriculum.
• J. Tanton. Breaking Through the Mathematics Education System Despite Itself. Medium, 28 Dec, 2018.
• The Limits of Curriculum Choice. Harvard Graduate school of Education.  March 11, 2019.
• Choosing a Math Curriculum. Mathscore.com

Ribos sąvoka

• Proving a Limit: x^2 = 4.  Video
• Epsilon delta limit. Video Dr. Peyam; In this video, I calculate the limit as x goes to 3 of x^2, using the epsilon-delta definition of a limit.
• Introduction to Cauchy Sequences