LET’S GET REAL: EFFECTIVE NUMBER TALKS IN ALGEBRA I
Tiffany J. LaCroix Sara Brooke Mullins
Virginia Polytechnic Institute and State University
Number Talks have grown in popularity since Parrish’s (2010) book on whole numbers, and her work on fractions, decimals, and percents (Parrish & Dominick, 2016). However, there is yet to be a major publication on using number talks in Algebra I. Since the Algebra I Virginia 2016 Mathematics Standards of Learning (SOL) document begins with a statement concerning the importance of Algebra I as a gatekeeper to advanced mathematics, and as number is the basis for all mathematical thinking, the usefulness of number talks in Algebra I is a natural point for learning and discussion for all secondary teachers. This article explains what a number talk is, how to do one, and why it is important to do number talks in Algebra I. Several examples of Algebra I number talks are also included as well as resources teachers can use.
WHAT IS A NUMBER TALK & WHY DO ONE?
A number talk is a 5 to 15 minute discussion about numbers at the beginning of class and can, but does not have to, be related to the daily mathematical goal. The classroom should be organized in small groups, so students can talk to each other, make eye contact with the speaker, and hear each other’s ideas. Also, all calculators, laptops, phones, and writing utensils should be put away since the focus is on mental math. Prior to beginning the number talk, the teacher must ensure the task is accessible to all students, and that there are multiple methods to reach the solution (Parrish & Dominick, 2016). If a task only has one method, it limits discussion possibilities. When choosing an accessible task, the teacher should anticipate different methods that lead to the correct solution, as well as those that lead to multiple incorrect solutions (Parrish & Dominick, 2016).
The number talk begins with students individually identifying methods for a solution by placing their fist in front of their chest, holding up their thumb when they have identified one method, the thumb and pointer-finger when they have two methods, and adding a finger for each additional method until personal think time is up. When the teacher sees that everyone has at least their thumb up, students volunteer to share their methods. This process ensures that every student has something to share with the class if they choose, and no one stops thinking because the students cannot see who has multiple methods. The teacher records the shared methods without judgement of incorrectness until several methods are shared. The teacher then asks questions about the shared methods until the mathematical relationship behind the number talk becomes clear to the class (Parrish & Dominick, 2016).
Number talks are beneficial for students for several reasons. First, they provide a safe environment where everyone can contribute to the math. This builds the confidence of everyone in the class; especially those students who may not feel able to contribute during a normal lesson (Parrish & Dominick, 2016). They also offer a chance for rich mathematical discourse where students can explain their thinking, ask questions, test strategies for reasonableness and correctness, investigate mathematical relationships, learn from mistakes, make connections between methods, and learn to choose efficient strategies (Parrish & Dominick, 2016). Most of all, it affords a chance for students to use their number sense (Parrish & Dominick, 2016), which is especially important since algebra is the study of how mathematical relationships cause numbers to covary. Number talks also give teachers a chance to listen to what students are saying about math, analyze student thinking, ask open-ended questions, and practice classroom norms where students listen, question, and respond to each other (Parrish & Dominick, 2016). They also firmly put the authority for mathematical ideas in the hands and minds of the students.
ALGEBRA I NUMBER TALK EXAMPLES
The first time a teacher uses a number talk, it is important to use an easy task because everyone in the class, including the teacher, will need a safe space to adjust to a new type of task and conversation. The first one we usually use is a grouping of 10-15 stars (or any object) that can be counted in several ways. The idea is to introduce students to algebra as the study of patterns, and reinforce that there are different ways to identify and explain patterns. Another number talk we use allows students to compare answers and reason with rational and irrational numbers. To help students practice the number sense around these skills, a teacher could ask students to explain how 5/7, 15/32, 14/31, 40/70 and are more or less than 1/2, or to explain how to order 3/8, 8, 36%, 16, 1 6/11, and 5/16 from least to greatest. Similarly, students could be asked to explain which fractions in a set are closer to zero, a half, or one, or which fraction in a pair is greater. Another concept students often struggle with is order of operations (Herscovics & Linchevski, 1994). Number talks can help facilitate conversations about this with tasks such as having students explain how to simplify 2(9 - 4) + 4 * 2. Similarly, having students explain which problem is not easy to work mentally like 2337 - 1337, 105(105) - 95(105), 1713 + 133, and 377 + 346 gives them the chance to talk about algebraic notation as well as order of operations (Bonato, 2016).
These suggestions all use number talks as a way to address numerical ideas in algebra indirectly, but number talks can also directly address SOLs. For example, having students explain different ways to simplify 45x4, or estimate the solution to 84 addresses SOL A.3 (Algebra I, 2016). Sometimes the number talk can grow organically from an algebra game such as “Guess My Rule” (2017). In this game, the teacher thinks of a rule, and has students guess x-values while the teacher fills in y-values on a chart. Students plot these points on a class graph. After a few rounds students guess y-values while the teacher fills in x-values. The discussion comes from students guessing the rule and explaining the different ways they figured it out.
Number talks for Algebra I do take time to develop or locate online since there is no significant publication on them yet. They will also take time to practice so students get used to mental computation, talking about numbers, and sharing their mathematical ideas. However, the gains students make in algebraic thinking and number sense are worth the time.
Algebra I. (2016). Mathematics standards of learning for Virginia public schools. Retrieved from http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/2016/stds/stds-algebra-1.pdf
Bonato, J. (2016). Number talks in the secondary math classroom [PowerPoint]. Retrieved from http://www.scoecurriculum.net/stemsymposium/documents/jbonato_NumberTalks.pdf
Guess my rule. (2017). The Charles A. Dana Center at The University of Texas at Austin. Retrieved from http://www.insidemathematics.org/classroom- videos/number-talks/5th-6th-grade-math-guess-my-rule
Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27, 59–78.
Parrish, S. (2010). Number talks: Whole number computation. Sausalito, CA: Math Solutions
Parrish, S., & Dominick, A. (2016). Number talks: Fractions, decimals, and percents. Sausalito, CA: Math Solutions