**By Jan Bryan, EdD, Vice President, National Education Officer & Brian Karsbaek**

The Romanian men’s soccer team gets it. Mathematics is both a systematic and social enterprise. In order to get Romanian children excited about math, and to address the 20% dropout rate among high school students, the Romanian soccer team substituted equations for integers to engage their younger math peers. The systematic processes required to solve each equation led to children following their favorite players and understanding the relationships among the numbers and symbols on their uniforms.

Indeed arithmetic is systematic. For something to be systematic, it is generally arranged in an ordered system and is concerned with classifications of items within that system. Ordered systems, such as a number line, and classifications, such as sorting numbers into whole, fraction, decimal, integers, etc., are at the core of arithmetic.

Indeed arithmetic is systematic. We lead students to be confident within this system through understanding of numbers and how they are classified. Some of the work involves memorization and applying consistent processes to manipulate numbers. Memorization is part of being systematic.

Learning 6 x 7 to a level of fluency prepares you to learn 6x = 42. If students lack math fact fluency and automaticity, algebraic reasoning may seem out of reach. One study found that 90% of incoming college freshmen lacked fluent and automatic recall of math facts, and without mastery of math facts students are denied access beyond minimal growth (Caron, 2007, DeMaioribus, 2011).

**Indeed arithmetic is systematic and, while it is the lowest branch of the discipline of mathematics, it sets the stage for all other work in mathematics.** But systems and systematic thinking represent part of the equation; a part of the whole.

Indeed arithmetic is systematic, but there is more to this equation…

As explained by Sun (2014), working with math requires that you know more than what a 9 is, but that you understand “how a 9 can relate to a 3 or 27, because math focuses on relationships and how numbers connect.” This same reasoning applies to domains within the discipline. For example, Algebra focuses on interactions among real and imagined objects by translating those objects into simple shorthand that explains how A relates to B (2007). In geometric reasoning, we seek to find the dynamic interaction among angles within a polygon or the relationship among circumference, radius, and diameter.

**Math is social in that it focuses on relationships.** Are you interested in the exact point in time Robert D’Niro’s career took an astounding new direction? Perhaps you are more intrigued by the relationship between location and purchase in Starbucks’ membership rewards program. Symbols, systems, and relationships make math social. To learn about D’Niro, Starbucks, and much more visit https://socialmathematics.net.

Social math classrooms are grounded in accepted systems for managing tasks and authentic mathematical discourse. As L. S. Vygotsky states, language, i.e., discourse, is the social representation of thought. For math to be social, it must be verbal and precise. For example, mathematicians don’t draw. They represent, provide information, label, diagram, use keys, and focus on scaling—but they do not draw (Hess, 2014).

The math genre promotes systematic thinking. Google the term “perimeter,” and click the Images link. Likely you find rectangles with ants marching around the sides—a well-wore mnemonic for remembering how to calculate perimeter. It is far more systematic to teach students what perimeter means (i.e., “peri” means around and “meter” means measure) and from that understanding lead them to reason through the measurement.

An effective social experience is rooted in powerful mathematical discourse, which is evident as students talk about their ideas and provide reasoning to support those ideas. Hess (2014) notes that engaging students in talking about math bring to light their thinking about and working with math. For example, a student may give a correct answer despite having an incomplete understanding. Conversely, a student may know more than a problem requires but still arrive at the wrong answer. Students may own “working on math” yet still, have room to grow in mathematical thinking and reasoning.

**Let’s keep this mathematics blog going by building a solution as a digital team!** Create an equation for each whole number from 1-50. The challenge is that you can only use the numbers 1, 2, 3, and 4; and you can only use each number one time. You may use addition, subtraction, multiplication, division, square roots, and exponents in your equations. For example:

(1 – 2) x (3 – 4) = 1

(2 x 3) – 4 – 1 = 2

(3^2 x 4) + 1 = 37

**Join the challenge! Comment your equations and answers below!**

Bieler, Des (2016, March 27). Romania’s soccer team puts math problems instead of player numbers on jerseys. *The Washington Post*. Retrieved from https://www.washingtonpost.com/news/early-lead/wp/2016/03/27/romanias-soccer-team-puts-math-problems-instead-of-player-numbers-on-jerseys.

Caron, T. A. (2007). Learning multiplication the easy way. Clearing House 80(6), 278-282.

DeMaioribus, C. (2011). Automaticity of basic math facts: The key to math success. Unpublished thesis. University of University of Minnesota Duluth. Retrieved from https://d commons.d.umn.edu/bitstream/10792/274/1/DeMaioribus,%20Carmel.pdf.

Heller, R. & Greenleaf, C. (2007). Literacy instruction in the content areas: Getting to the core of middle and high school reform. Alliance for Excellent Education. Retrieved from http://all4ed.org/reports-factsheets/literacy-instruction-in-the-content-areas-getting-to-the-core-of-middle-and-high-school-improvement.

Hess, K. (2014). How to go deep to meet the new math standards[Recorded webinar]. Retrieved from http://info.renaissance.com/Go-Deep-Recorded-Webinar.html?_ga=1.260384074.658388591.1470369717

National Council of Teachers of Mathematics (2010). Discourse. Retrieved from http://www.nctm.org/uploadedFiles/publications/write_review_referee/journals/mtms-call-Discourse.pdf

Sun, R. (2014, May 7). Social math: Why learning math involves more than writing numbers [Blog post]. Retrieved from http://www.huffingtonpost.com/robert-sun/social-math-why-learning-_b_5279935.html.

Vygotsky, L. (1978) Mind in Society: The Development of Higher Psychological Processes. Harvard University Press, Cambridge, MA.

Jan Bryan has more than 20 years of classroom and university teaching experience. Her work at Renaissance focuses on formative assessment, exploring data in a growth mindset, and literacy development.

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## 20 Comments

(4! x 2) +3 – 1 = 50

Nice!

What a great way to get students to love math!

Brian and I had a lot of fun writing the blog. Along the way, I got more and more drawn into mathematics. Exceptional teachers who make math social + engaged students = success!

I think if my teachers had subscribed to this theory, I might have been a math major!

Me too!

4×3\(1+2)=4…..4 days until school starts for me:)

Well done. And, it’s only (3*4) + (1+2) = 15 weeks until winter break.

Fun! My daughter’s wonderful 4th grade teacher just did a similar math challenge with her students and my daughter has talked about nothing else!

The academic partnership between a teacher and a student is the most impactful variable in student achievement. Here we see it in action. Please share my appreciation to this wonderful 4th grade teacher. This teacher is making a difference in students’ lives and just made my day!

3^2 + 4 = 13 (How many days I’ve been married!) ..I don’t know if I did my 3 squared correctly! lol!

For entering equations online, it’s fine. Congrats on your wedding and 13 days (and counting) of joy. Aim for nothing short of (1 * 2 * 3 * 4) ^ ∞. (OK, I cheated and added an infinity symbol.)

I love soccer and math!! Only (4*2)-3 until soccer season start for close to 300 kiddos!! I am a huge fan of Math Talk!

Thanks for the equation and the comments. Love the term “Math Talk.” There is a lot of discussion about “mathematical discourse”—all of it instructive and important, but “math talk” is such a welcoming concept. Imagine 300 soccer-playing, math-talking kiddos this fall. We need an equation for FUN.

What a great way to integrate math.

Absolutely—especially in the hands of a great teacher.

(4^2 + 1) -3= 14

This is my 14th year teaching.

Congratulations and well done. The research suggests that many teachers leave after (4-2) + 3/1 years. May you continue to engage and inspire our nation’s future leaders.

[(2 x 4) x 3] – 1 = 23 Only 23 days until my granddaughter is born!

This is exciting! Congratulations to you and your entire family. Just think, (4*3)*(2/1) hours after she is born, she will be exactly (4/2)/2/1 day old. Get ready to celebrate!