1
Aaron Keenlance
Professor Langeberg
EDUC 330
30 September 2014
Mathematical Content Literacy Philosophy
√−1 23 ∑ 𝜋 and it was delicious! One can probably interpret the symbols in order to
make sense of the sentence. Or is it even a sentence? The language of mathematics has evolved
into a form of natural language supplemented by a highly specialized symbolic notation for
mathematical formulas. Because of this, mathematics education relies heavily on content
literacy. Wise (2011 as cited in Vacca, p.14) states “adolescent literacy is the cornerstone of
students’ academic success.” Thus, mathematics education must promote literacy in ways that
encourage reading, writing, and speaking in order for learners to represent, communicate, and
comprehend mathematics in and out of the classroom.
Students learn differently and at different paces, each having their own needs and
interests. When I was studying mathematics during middle and high school, my math
instructors’ pedagogy followed a similar pattern – students sitting quietly in rows listening to the
teacher lecture, odd numbered homework exercises from the book every night, and procedurally
based tests at the end of each unit. The traditional approach that I grew up knowing does not fit
the needs of today’s adolescents as Vacca and Vacca (2011) state, “adolescents entering the adult
world in the 21st century will read and write more than at any other time in human history. They
will need advanced levels of literacy to perform their jobs, run their households, act as citizens,
and conduct their personal lives” (p. 14). Teaching strategies must be accommodating to
students’ different learning styles.
2
Although teachers teach from the same curriculum, they are allowed the freedom to
choose how they want to teach their students. After several field experiences at local schools
and extensive research, I have concluded that I follow the constructivist philosophy as a teacher.
Constructivism says that people construct their own understanding and knowledge of the world
through experiencing things and reflecting on those experiences. I believe that students construct
knowledge from what they hear, see, and do. The mathematics classroom is meant to be
interactive, social, and hands-on.
Collaboration is an essential part of my teaching philosophy. Collaborative learning
means that students are responsible for each other’s learning while working toward a common
goal. As a constructivist teacher I will follow Vygotsky’s Sociocultural Theory which suggests
that development depends on interaction with people and social interaction plays a fundamental
role in the development of cognition (McBride, 2011, p. 7). During group work students will be
actively exchanging, debating and negotiating ideas within their groups. This may include
students teaching one another, students teaching the teacher, and of course the teacher teaching
the students. They will construct their knowledge and transform it collaboratively, which in turn
will increase their interest in the topic. Socialization is necessary for group work to be effective
and for students to hear mathematical terms in language. I will advocate for socialization by
teaching strategies to become effective collaborators such as; jigsaw, think-pair-share, student
peer coaching, and various forms of group work.
In addition, the constructivist approach will allow students to take ownership in learning
while providing information and skills that are of interest to the student. According to Vacca and
Vacca (2011), “students’ motivation for reading and learning with texts increases when they
perceive that text is relevant to their own lives and when they believe that they are capable of
3
generating credible responses to their reading of the text” (p. 176). By allowing students to learn
through methods that they can relate to, their curiosity about the material will be aroused. This
curiosity will lead students to discover problems known as conceptual conflicts. And further, the
conceptual conflicts will need to be resolved. Finally, reading will be the key to resolving the
conceptual conflicts. As Vacca and Vacca (2011) state, “arousing curiosity helps students raise
questions that they can answer only by giving thought to what they read” (p. 181). Notice how
student ownership → motivation → curiosity arousal → conceptual conflicts → READING,
(where the arrows are a symbolic representation in math for the term “implies.”)
Mathematics has a complex vocabulary. This can lead to many problems for students
who are learning new topics as mathematics texts rely on a large amount of technical vocabulary.
As Massey and Riley (2013) state, “mathematics texts are written using language patterns that
differ from the narrative patterns many elementary students typically read. Terms have dual
meanings, both general and math specific” (p. 577). For example, references to a plane may
refer to a surface; however, in a story problem, the word plane might refer to an airplane. A
student can lack vocabulary knowledge but still be proficient with his computational skills.
However, the student will lack the ability to converse and explain mathematics. In addition,
developing mathematics vocabulary knowledge allows adolescents to expand their abstract
reasoning ability and move beyond operations to problem solving which are two important
qualities necessary to be a mathematically proficient student. Dunston and Tyminski (2013)
state that math vocabulary is inextricably bound to students’ conceptual understanding of
mathematics (p. 41). Thus, knowledge of math vocabulary is necessary for mathematics
achievement.
4
In addition, mathematics texts are multisemiotic: that is, they use natural language and
symbolic language (Massey, 2013, p. 578). Algebraic text uses traditional words and sentences
for explanations, sentences written with words and symbols for word problems, and sentences
written as only symbols such as 𝑦 = 1.5𝑥 − 5. Order is also crucial for understanding the text.
When solving many problems in mathematics, we must follow specific guidelines. One
important guideline we use often is known as the order of operations. In short, the order of
operations procedure rearranges a problem so we can solve it left to right on paper, similar to
reading a text left to right. Hence, if one does not follow this simple step, then the answer will
be incorrect. As seen, the language of mathematics is vastly different than the language of our
everyday lives, requiring students to handle these challenges in different ways. Through a
constructivist approach I will integrate reading, writing, and speaking into my classroom because
these processes are essential for language and concept development in mathematics.
In my future classroom, reading, writing, and speaking will be integrated into daily
lessons. There is a strong relationship between literacy and learning. Vacca and Vacca (2011)
define content literacy as “the ability to use reading, writing, talking, listening, and viewing to
learn subject matter in a given discipline” (p. 16). When comparing the definition of content
literacy to the description of a mathematically proficient student, we see many similarities. The
Standards for Mathematical Practice state that mathematically proficient students understand and
use stated assumptions and definitions, justify their conclusions, communicate them to others,
and respond to the arguments of others. Siegel, Borasi, and Fonzi (1998) believe that language is
important in inquiry-based, constructivist teaching because it provides “the symbolic resources
for members of a community to negotiate meanings and representations of their world” (p. 379).
Content literacy instruction is integrated into a constructivist teacher’s philosophy. Together,
5
they will engage students in problem solving and equip them to use mathematics efficiently,
creatively, and productively within a society. As a future teacher, I will strive to make every
student mathematically proficient by embedding content literacy strategies into my lesson
planning.
A great way to integrate reading into classrooms is through the use of think-alouds. The
purpose of a think-aloud strategy is to model the thinking process of a skilled reader. Thinkalouds are successful with strategies like making connections, using text features (illustrations,
headings, boldface), and dealing with difficult text. Vacca and Vacca (2011) state, “Students
will more clearly understand the strategies after a teacher uses think-alouds, because they can see
how a mind actively responds to thinking through trouble spots and constructing meaning from
the text” (p. 201). After the teacher models his thinking process, the students will practice thinkalouds with a partner. The sharing of thoughts between the students will provide socialization,
while increasing their depth of knowledge.
Math journals are a great way to incorporate writing into the classroom. Math journals
may include exploratory writing activities, summaries, letters, student-constructed word
problems and theorem definitions, descriptions of mathematical processes, calculations and
solutions to problems, and feelings about the course (Vacca, 2011, p. 296). Integrating math
journals into the classroom will allow students to use ordinary language along with mathematical
language in their responses. Math journals will reinforce strategic learning processes by having
the students write about their thinking.
𝑖 8 𝑠𝑢𝑚 𝑝𝑖 and it was delicious!, and, I ate some pie and it was delicious! are two ways
that the first sentence can be interpreted. I believe mathematical literacy is necessary for a
student to represent, communicate, and comprehend math problems. Mathematically literate
6
students draw meaning from symbolic representations and translate the meaning into thoughts,
sentences, and images. In addition, they demonstrate fluent transitions between converting
symbolic representations into thoughts, sentences, and images and vice versa. Through a
constructivist lens I will integrate content literacy into my teaching.
7
References
Dunston, P. J., & Tyminski, A. M. (August 01, 2013). What's the Big Deal about Vocabulary?
Mathematics Teaching in the Middle School, 19, 1, 38-45.
Massey, D., & Riley, L. (April 01, 2013). Reading Math Textbooks: An Algebra Teacher's
Patterns of Thinking. Journal of Adolescent & Adult Literacy, 56, 7, 577-586.
McBride, D. F. (2011). Sociocultural theory: Providing more structure to culturally responsive
evaluation. New Directions for Evaluation, 2011, 131, 7-13.
Siegel, M., Borasi, R., & Fonzi, J. (1998). Supporting students’ mathematical inquiries through
reading. Journal for Research in Mathematical Education, 29, 378-413.
Vacca, R. T., Vacca, J. A. L., & Mraz, M. E. (2011). Content area reading: Literacy and
learning across the curriculum. Boston: Pearson.