Strategies for Enhancing
Conceptual
Understanding in the
Mathematics Classroom
Lamont Holifield, M. Ed.
CICS-Ellison High School
Imathination Conference 2012
Saturday, January 21,2012
Agenda
 Rationale for Discussion/Connection to Common Core
 Tool You Can Use
 Integrating Literature into Mathematics
 Writing in the Mathematics Classroom
 Debate and Critique
 Questions/Answers
 Additional Resources
What’s The Message?
“Turn and Talk Activity”
Analysis of the Cartoon
Current Challenge
 Part of the challenge of teaching reading in Mathematics
stems from the confusion over what “reading
mathematics” actually means.
 Is it being able to read expressions with mathematical
symbols?
 Is it being able to comprehend printed numerical data?
 Is it being able to comprehend worded mathematical
passages in, say, a mathematics textbook?
Why Reading in the Mathematics
Classroom?
 First and foremost, it is paramount to meeting at least
three of the Standards for Mathematics Practice listed
in the New Common Core Standards:
 Students must be able to make sense of problems and
persevere in solving them.
 Students must be able to reason abstractly and
quantitatively.
 Students must be able to construct viable arguments and
critique the reasoning of others. Hence, the necessity of
using principles of academic debate and argumentative
reasoning skills.
Why Reading in the Mathematics
Classroom?
 Secondly, it requires unique knowledge and skills not
taught in other content areas.
 Typically students are taught to read from left to right.
This holds true in mathematics with several exceptions.
 In addition, they must know how to read from right to left.
For example, when reading an integer number line.
 They must know how to read from top to bottom. For
example, when analyzing a table of data.
 They must also know how to read diagonally. For example,
when reading a graph.
Why Reading in the Mathematics
Classroom?
 Thirdly, mathematics text contain more concepts per
word, per sentence, per paragraph than any other kind
of text.
 In addition, the concepts are abstract making it difficult
for readers to visualize their meaning.
 Fourth, authors typically write in terse and compact
style. Each sentence contains a lot of information and
there is a little redundancy. Students tackle the text,
at time, like a short story and miss significant details,
explanations and the underlying logic.
Challenges That We Face As
Mathematics Teachers
 Complexities of teaching mathematics in ways we did
not experience as students
 Discomfort with our own mathematics knowledge
 Lack of sustained professional development
opportunities like Imathination
 Greater requirement for facilitation skills and attention
to classroom dynamics
 Lack of time, especially in face of curricular demands
Recommended Novels/Books for
Integration into Mathematics
 Secrets, Lies and Algebra (Algebra I, II Classroom) by
Wendy Lichtman
 A Gebra Named Al (Algebra I, Chemistry) by Wendy
Isdell
 Flatland, A Romance of Many Dimensions (Geometry,
Pre-Calc) by E. A. Abbott
 The Numbers behind Numb3rs: Solving Crimes with
Mathematics (Statistics/AP Stats) by Keith Devlin
 A Certain Ambiguity (Pre Calc or Higher Mathematics) by
Gaurav Suri
Strategy #1
Integrating Literature into
Mathematics
 Students can make connections to text and engage in
learning mathematical terminology without realizing
that they are doing so.
 It allows students to experience mathematics in a nonintimidating manner. Consider the student who has only
had negative experiences with mathematics and finally
gets to experience it in a context he/she can enjoy.
Talk and Turn
 Based upon what you have heard, what can potentially
be the value added to students?
 How can incorporating the reading of novels and other
text potentially engage students in the learning?
 What challenges do you perceive?
Visit the Website below for other titles in mathematical
fiction:
http://kasmana.people.cofc.edu/MATHFICT/
Strategy #2
Using Writing in the Mathematics
Classroom
Quote from: Maggie Johnston, 9th Grade Math Teacher,
Denver, CO
“Writing in mathematics gives me a window into
my students’ thoughts that I don’t normally get
when they just compute problems. It shows me
their roadblocks, and also gives me as a teacher, a
road map.”
Talk and Turn
 What does the statement mean to you, personally?
 In the statement, I have underlined a couple of words.
Answer the following questions:
 What is the purpose of a window?
 Why is students’ thinking important?
 What is a roadblock? What is the danger of not seeing a
roadblock? What could potentially happen if a roadblock is
simply ignored?
 What is the value of a road map?
Ideas for How to Incorporate
Writing Into Mathematics
 “The Journalists’ Questions”
 Biography and Autobiography (Mathography)
 Learning Logs, Blogs and Journals
 Summaries (Venn Diagrams, Concept Maps)
 Magnet Summaries
 Explicitly Teaching Relevant Vocabulary
 Creative Writing in Trigonometry (can be integrated into
other mathematical subjects)
Strategy 3: Integrating Debate,
Discourse and Argumentative
Literacy
A Potential Transformative Model of the Math Classroom
Math Classroom functions as a community where
thinking, talking, agreeing and disagreeing are
encouraged. The teacher provides students with
powerful math problems to solve together and students
are expected to justify and explain their solutions. The
primary goal is to extend one’s own thinking as well as
that of others.
Talk and Turn
 What is your initial reaction to this model?
 Currently, how does this model fit as a description of
your classroom?
 What are some challenges to adopting this type of
model?
Ideas For Integrating
into the Mathematics Classroom
 Discourse Time! (What is It?/How does it work?)
 Debate in the Mathematics Class (Solving a System of
Linear Equation Methodology Debate)
 Error Analysis Work (Looking at Work/Listening at Peers)
 Moving from Teacher Driven to Student-Led Discussion
Questions/Answer Session
For more information on any and all strategies
introduced, contact me at:
Lamont Holifield
CICS-Ralph Ellison High School
1817 W. 80th Street
Chicago, IL 60620
lholifield@cicsellison.org
(773) 307-0734
Thanks For Participating In This
Discussion Today!