در ستایش علامت منفی ترجمه مقاله زیر است

Amir Asghari, In Praise of the Minus Sign , For the Learning of Mathematics, 40, 2, July 2020.

#### مقاله های فارسی

##### عنوان مقاله ها و خلاصه ی داده شده به انگلیسی است ولی لینک داده شده به اصل فارسی مقاله است

contexts for algebraization at primary school level

Written with my PhD student, Leyla Khosroshahi, the paper suggests a framework for connecting arithmetic to algebra, or better to say, doing algebra within arithmetic, in primary schools.

Fourth graders’ understanding of the equal sign

**درک دانش آموزان چهارم دبستان از علامت تساوی**

Written with Sharareh Dastjerdi and Maryam Adeli, the paper is exactly what the title suggests. Not surprisingly, the Iranian fourth-graders had the same understanding as nearly all the other primary students mentioned in the relevant literature: they had an operational understanding of the equal sign.

from arithmetic thinking to algebraic thinking

**گذر از تفکر حسابی به تفکر جبری**

Written with Kaye Stacey, The paper was mainly based on Kays’s research. We wrote it for Iranian teachers, using examples from Australian and Iranian context.

Written as part of a series of papers about the different roles of letters in

algebra, “A is Free” is to show how letters in the absence of a relevant structure might loose their meaning, but at the same time, might find freedom. Consider n+n+1+n=3n+1, it might represents two different ways of counting the same structure or …

Written as part of a series of papers about the different roles of letters in

algebra, “A is Absent” warns teachers and textbook authors about such careless uses of the so-called blanks (in different forms and shapes) and how they might be a source of confusion in the already hard journey from arithmetic to algebra. Think of different possibilities that you might be able to interpret something like blank + blank =2 blank…

Written as part of a series of papers about the different roles of letters in

algebra, “A is Silent” discusses the unproductive misuses of the standard exercise of translating something from words to the letters, from English (Farsi) to the symbolic language of algebra.

Written as part of a series of papers about the different roles of letters in

algebra, “A is Delicious”, based on the dissertation of Maryam Abdolahpour, my master student, discusses the side effects of the so-called fruit-salad algebra.

How to use Origami to enhance students’ algebraic thinking

**تاثیر اریگامی بر توسعه ی تفکر جبری دانش آموزان**

Written with Faezeh Falahat, one of my master students, the paper is exactly what the title suggests! In particular, our focus was on the hidden algebraic aspect of origami as the keeper of structures and relations between different elements of a figure while the size might change.

From 1 to 10, a way to understand numerical facts

**از یک تا ده، راهی برای درک واقعیت های عددی**

Written with Somayeh Shabani, one of my master students, the paper becomes the backbone of my algebraic theory, *specularity.*

history of Algebra, Book Review

This not a paper per se, but I thought it is better to be seated alongside the algebraic papers.

The Gains And The Pitfalls of Reification- The Case of Algebra, Translation

**داستان جبر: بخش اول؛ بخش دوم؛ بخش سوم**

This is the translation of the paper written by Anna Sfard and Liora Linchevski*. It was translated to accompany a number of my algebraic writings for teachers.

*Sfard, A., & Linchevski, L. (1994). The gains and the pitfalls of reification—the case of algebra. In *Learning mathematics* (pp. 87-124). Springer, Dordrecht.

#### Recreational Mathematics

##### ریاضیات بانمک و ترویجی

A tribute to Martin Gardner, in fact, the whole journal was published in honour of Gardner. Martin and I, or I and Martin was is written in Gardner’s style, adopting one of his works.

It is intuitively obvious was written to show whether something is obvious or not is dependent on one’s own intuition that may differ from one person to the other.

Comic Strip: Wow! Avicenna and Mathematics!

This is the first comic strip of a series of historical comic strips that I created based on the work of mathematicians. I used to call them fake histories since I was only true the development of mathematical concepts rather than the true story of the mathematicians involved in the development of the concepts. So there are cases in which two mathematicians who lived hundreds years apart coexist in the same frame as part of the story of the development of the concept!

Comic Strip: Our Irrational Brother

A mathematical-historical comic stripe about square root of two and the “person” who discovered it.

Comic Strip: Dots. Lines. Colours

**نقط ، خط، رنگ ؛ قسمت اول؛ قسمت دوم**

A mathematical-historical comic stripe about a famous conjecture in graph theory (i.e. the total colouring) around the life of Mehdi Behzad, the person who conjectured it.

Comic Strip: Mathematics in three moves

A mathematical-historical comic stripe around the work of Ebadollah Mahmoodian on mathematical aspects of *Sudoku* and Latin Squares.

#### Translations

##### ترجمه ها

From Arithmetic to Algebra : How to Teach Arithmetic Better

**از حساب به جبر، چگونه حساب را بهتر درس دهیم**

Written by Hung-Hsi Wu, this is the tenth *WikiLetter. *

LONG-TERM SENSE MAKING IN ARITHMATIC AND ALGEBRA

**مسیر طولانی ملموس شدن حساب و جبر**

Written by David Tall, this is the fifth *WikiLetter *translated by Yasaman Baghaei and I.

TENSION BETWEEN TEACHER & STUDENT ATTENTION

**توجه معلم کجاست، توجه دانش آموز کجا**

Written by John Mason, this is the second *WikiLetter ,*translated by Maryam Adeli and I.

A KEY TO DEVELOPING ALGEBRAIC THINKING: SEEKING, USING, AND EXPRESSING STRUCTURE

Written by Carolyn Kieran, this was the start of *WikiLetters*, translated by Sharareh Dastjerdy and I.

Logicomix: An epic search for truth

Logicomix is a must read for anyone interested in the foundation of mathematics, for all who have experienced doubt. I become in love at the first read. That is why I translated it, and in fact, I am the official translator.

**تحقیق ریاضی چگونه انجام می شود**

How research is carried out?, written by Michael Atiyah, that happens to be my academic grandfather 🙂 A very readable paper with a nice and unusual arguments in the favour of rigour in mathematics.

A metaphor for mathematics education

“A metaphor for mathematics education” is a very interesting paper written by Gerg McColm. In fact, the paper introduces more a metaphor for mathematics, rather than mathematics education. The paper is only four pages long, but it took a good time of Zahra Gooya and I to translate it.

The gains and the pitfalls of reification- the case of algebra

**داستان جبر: بخش اول؛ بخش دوم؛ بخش سوم**

Written by Anna Sfard and Liora Linchevski, The gains and the pitfalls of reification, proved to be very hard for the translation. We needed to create Farsi terms, the first one, for “Reification”. It took a few months from Zahra Kamyab and I to translate it. I think, one day, I do translate it again!

Success in Pure Mathematics, Differential Calculus and Applications

When I translated this one I was a master student, and I was paid about 5 pounds for the translation! At the time I was perhaps proud, being a maths teacher with a translation was better than being a maths teacher with no translation!