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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
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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
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