Guest Post by Pat Baltzley, MS/HS Math Coach

How do you get your students talking to one another? Do your instructional routines provide opportunities for student conversation around the mathematics of your lesson? One of the most critical practices we can implement in our classrooms is that of creating space for and encouraging mathematical discourse.

**Focusing on the Effective Mathematics Teaching Practices**

In 2014, the National Council of Teachers of Mathematics (NCTM) published *Principles to Actions* which outlines eight Mathematics Teaching Practices that “represent a core set of high-leverage practices and essential teaching skills to promote deep learning of mathematics” (p. 9). These practices provide the framework from which all mathematics teachers should hone their teaching craft. These eight Mathematics Teaching Practices are as follows:

- Establish mathematics goals to focus learning.
- Implement tasks that promote reasoning and problem solving.
- Use and connect mathematical representations.
- Facilitate meaningful mathematical discourse.
- Pose purposeful questions.
- Building procedural fluency from conceptual understanding.
- Support productive struggle in learning mathematics.
- Elicit and use evidence of student thinking.

Notice Teaching Practice #4: *Facilitate meaningful mathematical discourse.* The formal statement that accompanies this teaching practice is: “Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments” (*Principles to Actions*, p. 29). This is a very challenging practice to integrate into our classrooms as we navigate our scope and sequence, as we agonize over pacing and “getting everything in”, and as we strive to engage all students when instead we often feel like we are having to pull every word out of our students’ mouths.

**Integrating Mathematical Discourse into Classroom Routines**

So how do we go about providing our students with the opportunity to voice their understanding of math concepts, talk math with one another, and learn to carry the conversations themselves?

One of the easiest routines to integrate into our repertoire of mathematical discourse opportunities is Number Talks. I am talking capital “N” for Number and capital “T” for Talks. This is a very specific instructional strategy that develops a routine around eliciting students’ thinking from a mental math activity. This 10- to 15-minute routine guides students through finding an answer to a problem in their heads, then sharing their answers and, more particularly, their strategies for finding these answers, with the whole class.

**Using this strategy changes the teacher’s role from being front and center as the main conversant to a less central role as facilitator and recorder of student responses.** By asking questions to help students make meaning of their answers and strategies, teachers provide a great vehicle to help students solidify their number sense, learn new ways of thinking about numbers from their peers, and verbalize their thinking in an environment of trust.

Although a Number Talk has traditionally been viewed as an elementary instructional strategy, in recent years it has been growing as a viable opportunity at the secondary level to address skill gaps, illuminate misconceptions, uncover multiple strategies for approaching a solution, or formatively assess students’ growing understanding of a new concept.

Number Talks can be as easy as identifying a pattern from dots viewed for 3 seconds with students sharing strategies for how they saw the total number of dots. Or, they can be solving operational expressions such as 114 + 517, 12 × 18, 3 ½ × 4, or 45% of 120. They can be challenges such as finding three numbers with three different operations that equal -12. Or, they can be pictorial images that have students deciding, for example, which one doesn’t belong. Explore the website *Which One Doesn’t Belong* for problems like the ones below to create powerful Number Talks.

There are excellent resources available for learning more about Number Talks. The following resources provide guidance and suggestions for implementing Number Talks into both elementary and secondary mathematics classroom.

Sherry Parrish has been guiding the implementation of Number Talks into the elementary grades with her Number Talks book from 2010 and then in collaboration with Ann Dominick in 2016.

Ruth Parker and Cathy Humphreys provide thoughtful resources for teachers in grades 3-10 to consider as they look to integrating a Number Talk into their regular routines.

For secondary classrooms, the resources below, available at www.thumbsupmath.com, were developed in high school classrooms and can easily be integrated into middle school as well.

**Exploring Other Vehicles for Mathematical Discourse**

What other vehicles can we use to increase the opportunity for mathematical discourse in our classrooms? I am sure that somewhere in your teaching experience you have used a Think-Pair-Share (T-P-S). This seasoned instructional strategy is used as a collaborative learning opportunity that allows students to first think about a response/answer to a question/problem on their own, then pair with another student to share and engage in mathematical conversation about their responses, and finally share responses with the whole class.

If you’ve forgotten about this strategy, you might need to bring it forward in your routines again! Maybe you used to use this strategy and you became bored with it – there are plenty of ways to mix it up! Here are several websites that I found that rejuvenated T-P-S for me:

- 10 Fun Alternatives to Think-Pair-Share
- How to Use Variations on Think-Pair-Share in the Secondary Classroom
- Think-Pair-Share Variations

My new favorite variation of Think-Pair-Share was shared by Sara Van Der Werf in her mathematics blog. It is an instructional move called Stand and Talk that gets the students up and out of their seats to find a partner after their individual think time. In a focused way, the partners notice and describe something that is identified by the teacher. Read Van Der Werf’s description of this instructional move on her blog for implementation strategies and more details on this refreshing variation of T-P-S.

There are many other ways to purposefully facilitate discourse in your mathematics classroom. The important thing is that we create environments in our classrooms where students are active and valued members of the discourse community. As teachers, we must build an environment of trust and collaboration in which students are willing to put forth their mathematical explanations and strategies. Students must learn to consider the responses of others in the classroom, listen carefully to each other, and critique the reasoning of their classmates with respect and genuine interest.

Try a new vehicle for mathematical discourse a Number Talk or a variation on Think-Pair-Share, such as Stand and Talk, in your classroom today! Get those kids talking with one another and sharing their mathematical ideas!

**Meet the Blogger**

Patricia (Pat) Baltzley has spent over 40 years in education from teaching high school mathematics in Maryland, to mathematics program development at Johns Hopkins University in Baltimore, Maryland to curriculum and instruction supervision in Baltimore County. Pat worked as part of the mathematics leadership team in Montana’s Office of Public Instruction during 2012-2013 and worked as a Montana Common Core Standards liaison during 2013-2016. Pat is a school board trustee for the Gardiner Public School district, where she currently resides.

Resources:

- NCTM. (2014).
*Principles to Actions: Ensuring Mathematical Success for All.*Reston, VA: The National Council of Teachers of Mathematics. - Parrish, Sherry. (2010).
*Number Talks: Helping Children Build Mental Math and Computation, Grades K-5.*California: Math Solutions. - Parrish, Sherry and Dominick, Ann. (2016).
*Number Talks: Fractions, Decimals, Percentages.*California: Math Solutions. - Humphreys, Cathy and Parker, Ruth. (2015).
*Making Number Talks Matter: Developing Mathematical Practices and Deepening Understanding, Grades 4-10*. Portland, ME: Stenhouse Publishers. - Parker, Ruth and Humphreys, Cathy. (2018).
*Digging Deeper: Making Number Talks Matter More, Grades 3-10.*Portland, ME: Stenhouse Publishers.

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