Running Head: NUMBER TALKS 1

Number Talks to Build Mental Math and Computational Fluency

Margaret-Ellen Laettner

Kennesaw State University

NUMBER TALKS 2

Number Talks to Build Mental Math and Computational Fluency

Since the advent of the Common Core State Standards Initiative (Common Core State

Standards Initiatives[CCSSI], 2010), educators and school districts across the country have

been searching for improved and effective teaching methods that address the rigor that is

emphasized in the standards. The CCSSI (2010) has developed eight mathematical

practices in which it is important that students understand mathematical concepts more

deeply and can communicate their mathematical reasoning (CCSSI, 2010). One such

teaching method is “Number Talks”. While “Number Talks” in this literature review is a

specific program by Sherry Parrish, the basic methodology stems from the works of social

learning theorist, Albert Bandura, other researchers work regarding metacognition, and

classroom discussion, as well as recommendations from the National Council of Teachers of

Mathematics (National Council of Teachers of Mathematics[NCTM], 2000). It is my belief

that daily number talks, or mental math metacognition discussion, will have an effect on

mental math strategy acquisition and computational fluency in third grade EIP students.

The following review of literature supports the progression from Bandura’s social learning

theories to the present-day “Number Talk” teaching method.

Social Learning Theory

Children often imitate adults and other children. They imitate dress, speech, ideas,

likes and dislikes. In 1961, Albert Bandura conducted an experiment called “The Bobo Doll

Experiment”. On the website, Simple Psychology (2014), I observed video from Bandura’s

original experiment. The experiment had children observe an adult who displays

aggression toward a blow up “Bobo” doll. Subsequently, when the children played alone,

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they displayed aggression towards the doll imitating the actions of the adults they had

observed. “The findings support Bandura’s Social Learning Theory. That is, children learn

social behavior through watching the behavior of other children” (2014). In Morgan,

Rendell, Ehn, Hoppitt, and Laland (2012), researchers theorized about the evolutionary

basis of human social learning; the researchers assigned computer-based tasks to the

subjects. One group of subjects saw no demonstration of the task. The other group of

subjects saw a demonstration of the task first. The findings gave strong support to the

theory that social learning is genetic and that humans have evolved with this behavior.

Metacognition

Metacognition is thinking about your thinking. While engaged in number talks,

students must verbally communicate their thinking process (metacognition) and reasoning,

to justify their response. Just engaging in casual conversation does not necessarily

promote metacognition. Teachers must carefully and purposefully model the process

through “think-alouds”. They must also use direct questioning techniques to focus

responses from students. In Callahan and Garofalo’s (2014) research report, the authors

stated that in recent years, “math educators have begun studying the role of metacognition

in the performance of mathematical tasks” (p.22). They advise that teachers must design

their instruction to develop metacognition. The teacher can have students reflect on and

report their mathematical thinking. Bandura, Barbaranelli, Caprara, and Pastorelli’s

(1996) study entitled “Multifaceted Impact of Self-Efficacy Beliefs on Academic

Functioning” researched how student’s perception under various circumstances is

changed. Bandura found that “metacognitive training aids academic learning” (p.1219).

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Fletcher and Carruthers (2012) hypothesized that metacognition is acquired through

individual and cultural learning. They concluded that metacognition varies by individual

and culture. In the normal course of their day, people do not think about their thinking

processes. “Others appear to do so largely as a result of explicit cultural training (such as

courses in mathematics, logic, or scientific method)” (p.1368). Onu, Eskay, Igbo, Obiyo, and

Agbo’s (2012) quasi-experimental research of Nigerian primary school children sought to

observe the effect of metacognitive training. The control group learned math with

traditional instruction, while the experimental group received “Math Metacognitive

Training”. “The result of the study showed that training in math metacognitive strategy

improved pupils’ achievement in fractional mathematics” (p. 316).

Johnson, Ivey, and Faulkner’s (2011) article “Talking in Class” is primarily a

commentary on teacher modeled thinking. A teacher verbally expresses his or her own

metacognition, which in turn helps students with their own thinking. The authors

recommend several methods to increase the discussion and talk in a classroom. Teaching

strategies developed for special needs students, benefit general education students as well.

Mitchell (2013) outlines 20 evidence-based strategies for enhancing learning. He advises

behavioral, social, and cognitive strategies. Cognitive strategies are ones in which the

learner constructs their own understanding. Cognitive Strategy instruction includes

teaching a variety of skills, which include metacognition.

Classroom Discussion

After students learn how to communicate their thinking strategies, they will be

better equipped to participate in classroom discussion. The Math Principles and Process

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Standards (NCTM, 2000) communication standard states that students should be able to

organize their mathematical thinking, communicate that thinking to teachers and peers,

analyze and evaluate their own strategies and the strategies of others and be able to use

mathematical language appropriately. One way that teachers bring communication into

the classroom is through literacy. McKeny and Foley (2013) wrote of engaging children by

using literature in the classroom. Part of that process was the discussion of the literature

and the connections children make. They said, “…young students can begin to recognize,

analyze, compare and reason as they engage in personal experiences and shared stories”

(p.320). In Barnes’ (2010) retrospective essay, “Why Talk is Important”, the author states

that talk shapes knowledge through engagement. In addition, talking contributes to

understanding of a topic by reshaping what you already know into a new synthesis.

Talking helps students to try out different ways of thinking. Finally, he recommends,

“teachers lead by questioning so that students look critically at their own thinking and see

if it matches their existing perceptions” (p. 9). Cone’s (1993) article for the NCTE focuses

primarily on creating an atmosphere in the classroom in which students are not

intimidated by talk. She reported how she restructured her curriculum so that all students

would feel comfortable to ask questions and share their ideas. She supports her account

through observations of a student in her class who felt intimidated to talk, but gradually

felt more comfortable after talking one on one, then in a small group and then eventually,

the whole class. Heyman (1983) observed that a teacher soliciting further explanation

would utter, “What do you mean by that?” His belief is that students may not ever convey

the idea or answer that the teacher is searching. He states that teachers, “need to be

explicit in the formation of questions and acceptable model answers, as they expect their

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pupils to be in formulating their responses” (p. 41). Mueller and Maher’s (2009) research

on learning to reason, theorized that reasoning and proof form the foundation of

mathematical understanding. Research conducted at an after school program with African

American and Latino youths involved students working collaboratively on their problem

solving abilities. Problem solving discussion was one of the methods employed by the

researchers. They found that “the act of presenting justifications to the community and

listening to the arguments of others seemed to prompt students to challenge each other’s

assertions which in turn led to stronger arguments” (p.29).

The Ontario Canada Ministry of Education (2006) Guide to Effective Instruction in

Mathematics states that students who engage in mathematical talk gain experience in

reflecting and reasoning. “Oral communication includes talking, listening, questioning,

explaining, defining, discussing, describing, justifying, and defending” (p.6). When children

participate in the activity, they are deepening their understanding of mathematics. In the

Literacy and Numeracy Secretariat’s (2010) Capacity Building Series for Ontario Schools,

mathematics communications was one of the instructional tools recommended for use. In

the publication, they advise that teachers must coach their students on how to participate

in math discussions. Within this process, teachers need to ask clarifying questions so that

students can articulate their reasoning. In her journal article, Falle (2004) says that

language arts questioning techniques be used during mathematical discussion between

students. Students typically rely on inference and non-verbal cues for the understanding of

others, but that the teacher must model appropriate math language. Brown and Hirst

(2007) acknowledge, “…classroom talk is regarded as essential in engaging and developing

student understandings in the domain of mathematics” (p. 18). Their study, conducted in a

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primary school in Australia, analyzed how two-teachers used classroom talk to scaffold

student learning in math. Their findings were that the classroom talk helped students to

link their ideas to the conventions of mathematics. Cummings et al. (2009) studied pre-

kindergarteners and the relationship of math talk to their readiness skills and math

achievement. They used the “Building Blocks” program, which facilitates children’s

engagement through participation and talk. They concluded that in order for children to

benefit from math talk, the classroom teacher must have a control over the activities and

conversations of the children. Phyllis and David Whitin (2008) wrote an article detailing a

unit of study aimed at providing children experiences with solving problems. Children had

opportunities to solve mathematical problems and display their solutions through writing

and verbal explanation. One of Whitins’ implications for classroom instruction was to

allow children to talk about their work through their investigation. “By letting them explain

their reasoning, teachers can better assess their thinking. In fact, children will often revise

their answers as they share their reasoning aloud” (p.432).

Number Talks

Incorporation of social learning, metacognition, and classroom discussion is

essential what the program “Number Talks” is. Students share their mathematical

metacognition with their classmates in order to build their mental math and computational

fluency skills in an educational mathematical teaching process. The NCTM (2000) defines

computational fluency as having efficient, flexible and accurate methods for computing. In

her book, Number Talks, Parrish (2010) says that she developed this specific program in

response to teachers requesting a way to facilitate classroom discussion regarding mental

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math fluency. During number talks, students communicate their thinking to their peers.

Students must also be able to justify their reasoning with strategies that they have

developed (Parrish, 2011). In their article “Writing, Sharing, and Discussing Mathematics

Stories”, authors Kilman and Richards (1992) walk us through a classroom scenario in

which students work collaboratively on authentic mathematical “stories” or problems.

When solving these problems, children are encouraged to draw diagrams, write and

verbally share their thinking with their peers. During the discussion, the students are

using many problem-solving skills. They are seeking, interpreting, and evaluating

information. Their answer is not just a solution, but also an explanation of their thinking.

The authors also recommend that teachers model mathematical thinking with “think

aloud” examples. Marilyn Burns (2007), founder of Math Solutions, says that mental math

is a very important skill. Solving problems without pen and paper will get children ready

for the adult world. She has a program similar to “Number Talks”, called “Hands on the

Table Math”. Her process guidelines have four steps: (a) students must solve the problem

in their heads; (b) they then do it together as a class; (c) everyone shares their ideas and

listens to others; (d) teacher records responses on the board. Mathematic Solutions (2014)

also has a similar retail program to Number Talks called “Math Talks”. On their website,

Math Solutions claims math discourse is important to the common core state standards. “…

by promoting the use of dialogue and conversation to explore mathematical thinking. Math

Talk provides students an opportunity for deeper understanding through communication”

(Math Solutions, 2014). Russell (2000), in her article “Developing Computational Fluency

with Whole Numbers”, writes about how students solve problems differently. “Being able

to solve problems in multiple ways means that one has transcended the formality of an

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algorithm” (p. 155) and can make connections between mathematical ideas. Teachers need

to help students develop both mathematical procedures as well as efficiency in calculation.

Postlewait, Adams, and Shih (2003) believe that development of computational fluency and

number sense should be at the center of student activities rather than rote memorization

and algorithmic procedures. In order to promote meaningful mastery of math operations,

teachers should provide students with those opportunities, one being the opportunity to

participate in number talks. Young (2005) recommends that number talks be part of a

classroom’s daily routine.

Conclusion

In conclusion, the literature shows that the elements of the “Number Talks” teaching

method were successful ones. Social learning improves student engagement and

achievement when students imitate the positive aspect of another student. Metacognition

helps students to analyze what they are thinking so that they can better explain themselves

and understand others. Finally, classroom discussion incorporates communication

through language with speaking and listening. Children will understand concepts more

deeply if they discuss them. One thing that they all had in common was the teacher as

facilitator. Teachers must first model thinking and discussion strategies, and then

purposefully design discussion so that students learn effectively.

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References

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self-efficacy beliefs on academic functioning. Child Development, 67(3), 1206-1222.

doi:10.1111/1467-8624.ep9704150192

Barnes, D. (2010). Why talk is important. English Teaching, 9(2), 7-10. Retrieved from

http://search.proquest.com.proxy.kennesaw.edu/docview/926190858?

accountid=11824

Brown, R., & Hirst, E. (2007). Developing an understanding of the mediating role of talk in

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Cone, J. K. (1993). Using classroom talk to create community and learning. The English

Journal, 82(6), 30-38. Retrieved from http://www.jstor.org.proxy.kennesaw.edu/

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