Annotated Bibliography
Numeracy – Building a Community of Practice K – 12
The following is a brief listing of possible articles that may continue a discussion around numeracy with your team. It is by no means exhaustive
and serves as a starting point to spur thought and reflection. In the spirit of reflection, it is expected that teams will add to this list and share with
others as we continue to collectively move forward with this learning.
ARTICLES
Ali, R. (2010). Effect of using problem solving method in teaching
mathematics on the achievement of mathematics students. Asian
Social Science 6 (2), 67-72.
The purpose of this quantitative study is to investigate the effects of
using the problem solving method on grade eight students in public and
private elementary schools in Pakistan. There was a significant difference
between teaching concepts in the traditional method versus the problem
solving method. The author presented referenced literature to support his
purpose. The conclusions were based on student scores on mathematics
achievement tests. Knowledge, comprehension and application were areas
assessed for the purpose of this study. There were recommendations
offered by the author based on his findings and these included changing the
focus of textbooks to problem based learning, using problem based learning
in the classroom to improve student achievement and to prepare teachers
to include problem based learning into their practices.
Arcavi, A. (2002). Chapter 2: The everyday and the academic in
mathematics. Journal for Research in Mathematics Education.
Monograph, 11, Everyday and Academic Mathematics in the
Classroom, 12-29.
The author examines “everydayness, “mathematization” and
“context familiarity” in connecting/integrating mathematics between the
classroom and the “outside world”. These three concepts are explored in
more detail in the body of the article. Examples of each of the three
concepts are drawn from the author’s work with pre-service teachers,
curriculum development and research literature. Abraham Arcavi does
include “Academic Everydayness” as part of the “everydayness” in teaching
mathematics by illustrating two graphical solutions to an equation as
provided by teachers. The author proposes the need for considering
different practices and approaches in delivering the curriculum especially in
the area of “Academic Everydayness”. Accompanied by examples, the
theme of students finding different solutions to a mathematical problem are
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further explored in the “mathematization” and “context familiarity”.
Attard, C., & Northcote, M. (2011). Mathematics on the move: using mobile
technologies to support student learning (part 1). Australian
Primary Mathematics Classroom. 16 (4), 29-31.
This is an article focusing on the use of iPod Touch and iPad in the
primary mathematics classroom. The authors emphasize the importance of
pedagogy driving technology and not in the reverse case. Rocket Math,
Geometry Test, Maths Addicted, Basic Math and MathBoard Addition were
apps that the authors deemed appropriate for increasing number
operations. The following five apps: Red Dragonfly Mathematics Challenge,
Kenken: Train Your Brain Lite, LetsTrans Lite, Dice Puzzle and Sukoku are
briefly described and commented on their potential pedagogical value for
problem solving in the classroom. 2011 World Fact Book, iBluepring,
iBrainstorm, Keynote and Show Me were potential tools for the students to
use as apps where pedagogy drive technology. This article provides teachers
a snapshot into selecting tools for a problem solving mathematics classroom.
Attard, C., & Northcote, M. (2012). Mathematics on the move: using mobile
technologies to support student learning (part 2). Australian
Primary Mathematics Classroom. 17 (1), 29-32.
Global positioning system (GPS) and other hand-held devices’ uses
in the primary classroom are the focus of this article. Position of individual,
distance travelled, time travelled, speed and estimated time remaining to
destination are some information provided by the GPS. Together with this
information students could use the GPS like a pedometer and make
appropriate calculations. Webcams on the internet are also mentioned to
provide potential mathematical exercises for teachers. A hand-held infrared thermometer could be used for measuring temperature and then
connected to a laptop for subsequent mathematical tasks. The authors
introduce the readers to tools that could be used indoors or outdoors and
complement computational strategies in the mathematics classroom.
Benzanson, C, & Killion, J. (2001). Moving math outdoors. Green Teacher 64
(Spring), 31-33.
The question “When am I every going to use this?” leads the article.
The backdrop is the schoolyard. The authors provide a case for engaging
students in mathematics outside of the classroom. Example primary grade
activities cover the following concepts: patterns, number sense, geometry,
measurement and graphing. Example intermediate and middle grade
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activities cover the following concepts: collecting and describing data,
number operations, geometry, measurement and estimation. A detailed
lesson on the topic of sampling a plot of land is included in the text. The
authors provide a starting point for teachers to make use of their respective
schoolyard.
Bruno, J. (2011). Math movement: The integration of geometry and dance.
Hofstra University). ProQuest Dissertations and Theses, Retrieved
from
http://search.proquest.com/docview/877593961?accountid=14771
This Master of Arts in Elementary Education dissertation
investigates the improvement of skills levels in dance and mathematics. The
participants in the study are grades three and four students. The dance
classes were held in a neighbourhood dance studio. Geometric concepts
and spatial thinking are infused in the study. There are pre and post
comparisons concluding with benefits in skills development in math and
dance. Seventeen detailed lesson plans are included in the appendix as well
as a rubric to assess learning goals.
Busadee, N., Laosinchai, P., & Panijpan, B. (2012). Finding possibility and
probability lessons in sports. The Mathematics Teacher 105 (5),
372-378.
The application of sports into the teaching of probability is the focus
of this article. The concepts of permutations and combinations were taught
using table tennis, soccer (x2), track relay, football and golf. A description of
each problem is given to the reader accompanied by the solution. An
extension problem with golf is included in the article. The lesson was over a
five one-hour time period. The authors tested the sequence of the lesson
twice and used a control group to find improvements in test scores.
Civil, M. (2002). Chapter 4: Everyday mathematics, mathematicians’
mathematics, and school mathematics: Can we bring them
together? Journal for Research in Mathematics Education.
Monograph, 11, Everyday and Academic Mathematics in the
Classroom, 40-62.
The article explores the union between a mathematician’s math
and mathematics for children outside of the classroom through an
exploratory study involving a fifth-grade class. The author recognizes the
importance of the mathematics in the classroom but acknowledges that
there is also a need to integrate and provide activities that connect
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mathematics from student experiences outside of the classroom. Answering
the question: “(At least) three kinds of mathematics?” the author provides a
brief literature survey and characteristics on “School Mathematics”,
“Mathematicians’ Mathematics in the School Context” and “Everyday
Mathematics”. The teacher and the author developed a thematic module
involving games with an attempt to address students’ experiences outside
the classroom on the topic of geometric patterns. The next part of the
student involved the teacher introducing the concept of geometry which
included examining patterns and incorporating related activities in Native
American art. Tessellations were the final area of study for the class. The
study found that there was greater student participation in “everyday”
mathematics but an increase when there were mathematical discussions
with peers in the academic matters part of the module.
Edelson, R. J., & Johnson, G. (2004). Music makes math meaningful.
Childhood Education 80 (2), 65-70.
The article focuses on the interdisciplinary nature found between
music and mathematics. The authors endorse the integration of music and
mathematics. Activities through song and musical instruments are used to
connect pupils with mathematical concepts involving patterns, serial order,
graphing, sorting, classification and Venn diagrams. The concept of fractions
is incorporated by creating a musical arrangement with partial notes is one
example of a cross-curricular activity for the students. The integrated
activities provide examples of addressing the kinesthetic and auditory types
of learning. The strategies implemented and the selections of musical
instruments allow the students to represent and communicate their
understanding of mathematical concepts. The examples are descriptive in
nature and are not presented in a step by step lesson plan format. However,
the article offers a starting point for teachers to actively engage and connect
students with music as they learn mathematics.
Edens, K., & Potter, E. (2007). The relationship of drawing and
mathematical problem solving: Draw for math tasks. Studies in Art
Education 48 (3), 282-298.
This academic study examines children’s drawings with their spatial
understanding and problem solving in mathematics. Findings show “…that
level of spatial understanding and use of schematic drawings both were
significantly correlated to problem solving performance” (p. 282). The study
is supported by research. There are samples of children’s drawings in the
article. Teaching strategies are included by the authors. An extensive
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reference list accompanies this article for an expanded search for related
literature.
Edwards, A., & Ruthven, K. (2003). Young people’s perceptions of the
mathematics involved in everyday activities. Educational Research
45 (3), 249-260.
This is an exploratory study involving grade seven and ten students’
perceptions of mathematics in five “everyday” activitiesDressmaking/Making trousers, playing snooker/pool, knitting a cardigan,
making a Lego robot and playing chess. The data was based on interviews
with the participants. The study did find that the students were able to
identify mathematics more in the dressmaking/making trousers activity than
the others. However, there were mathematical concepts identified for each
activity with measurement and angles being the most frequently mentioned
by the students. The study provides a reflective educator to consider the
importance of selecting tools and strategies that integrate mathematics and
“everyday” mathematics.
Gainsburg, J. (2008). Real-world connections in secondary mathematics
teaching. Journal of Mathematics Teacher Education 11 (3), 199219.
Gainsburg, identifies the initiatives and a range of practices with
“real-world” connections and mathematics teaching. There is a
comprehensive list of literature connected to this topic. Sixty-two secondary
school mathematics teachers were surveyed regarding their understanding
and use of “real-world” connection in their classrooms. Five teachers were
chosen for further investigation concerning their respective practice. The
teachers were asked for written descriptions in the following categories:
Format- The teaching mode in which the connection was made; Feature- Any
special aspect enhancing the authenticity of the connection; Context- The
real-world setting or object to which the mathematics was connected; and
Mathematics- The mathematical concept or skill involved. The study did
show that a proper design and integration of “real-world” connections
provides “…a strong foundation for learning mathematical ideas.”
Harrell, G. K. (2008). Integrating mathematics and social issues.
Mathematics Teaching in the Middle School 13 (5), 270-276.
Harrell looks to local issues that would connect with the math
curricula. The main subject in this article is the construction of new roads.
The author provides descriptive examples of the mathematics that would be
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involved such as calculating the necessary acreage to build a road. Sample
calculations are included in the text. The students would also be asked to
role play civic officials in the debate of whether a road should be built or
finding an alternative route. The middle school mathematics teacher will find
this material to be jumping off point for potential ideas connecting social
studies and mathematics.
Heavey, J. M. (1998). The effects of integrating literature and mathematics.
Fairleigh Dickinson University). ProQuest Dissertations and Theses,
35 p. Retrieved from
http://search.proquest.com/docview/304470763?accountid=14771
This Master of Arts in Teaching dissertation examines the
integration of literature and mathematics through a study of grade one
pupils on the topic of measurement using books with mathematical
concepts. The author writes: “The perception of math changed as its
relevancy and practical applications became apparent. The learning
atmosphere was charged with enthusiasm and participation because the
students understood the reason why they were seeking a solution.” A
“Recommended Books for Teaching Math” was included in the Appendix as
well as a lesson plan and a worksheet. The paper provides supporting
research for integrating literature and mathematics. In conjunction with the
application of literature, the author also promotes the appropriate
classroom environment for making connections.
House, P. A. & Coxford, A. E. (Eds.). (1995). Connecting Mathematics across
the Curriculum. Reston, Virginia: National Council of Mathematics
of Teacher of Mathematics.
Though the yearbook was published in 1995, the cross-curricular
theme of mathematics is applicable today. This reference is intended for K12 teachers. The book is divided into five parts: “General Issues”,
“Connections within Mathematics”, “Connections across the Elementary
School Curriculum”, Connections across the Middle School Curriculum”, and
“Connections across the High School Curriculum”. The articles provide
suggestions for activities with accompanying descriptions in text and in some
cases with graphics. References are provided at the end of each article. In
total there are 26 articles.
Moschkovich, J. N. (2002). Chapter 1: An introduction to examining
everyday and academic mathematical practices. Journal for
Research in Mathematics Education. Monograph, 11, Everyday and
Academic Mathematics in the Classroom, 1-11.
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The two purposes served for writing the articles were to address
the juxtaposition of academic mathematical practices and everyday
mathematics in the mathematics classroom. The author expands the
discussion by including school mathematics and workplace mathematics into
the vernacular. Moschkovic presents two proposals: problems and activities
from workplaces and students’ experiences outside of the school; and
“making generalizations across applied problem situations.” The author
then proceeds to provide literature references connected to each proposal.
In the end, Moschkovic states, “…classroom teachers can connect students’
practices to the practices of mathematicians…teachers can connect
mathematicians’ practices to students’ classroom activities by encouraging
them to find or pose problems about mathematical objects, make
generalizations across situations, and construct mathematical arguments.”
Northcote, M. (2011). Step back and hand over the cameras! Using digital
cameras to facilitate mathematics learning with young children in
k-2 classrooms. Australian Primary Mathematics Classroom. 16 (3),
29-32.
Northcote provides an argument for the use of digital cameras as
tools in teaching mathematical concepts in the primary classroom. There are
cited references included in the case for using the digital camera. Examples
are included for the reader to use in the classroom: graphing by using
photos of shoes; space and geometry concerning symmetry, parallel, vertical
and horizontal lines; a math photo journal where student write reflections or
interpretations of their photos in the context of math concepts such as
shapes, counting, positions etc. Activating prior knowledge for the student is
also covered in the article. The author provides the reader with a starting
point for the potential uses of the camera in the classroom. “Real world”
mathematics certainly connects with classroom mathematics in this article.
Piatek-Jimenez, K., Marcinek, T., Phelps, C. M., & Dias, A. (2012). Helping
students become quantitatively literate. The Mathematics Teacher
105 (9), 692-696.
The authors define the meaning of quantitative literacy (QL);
question whether it should be incorporated into the traditional classroom;
how it differs from the traditional mathematics course and provides sources
of quantitative learning problems that could be used in middle school, high
school and college curricula. Content, context, teaching methodology and
assessment are elaborated on in the explanation to differentiate QL from the
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traditional way of teaching mathematics. The authors advocate the
inclusion of “Real-world” mathematics in promoting quantitative literacy.
Examples of sources such as newspapers, student journal entries, and
problems supporting QL are included in the article.
Rose, T. D., & Schuncke, G. M. (1997). The link between social studies and
mathematics. The Clearing House 70 (3), 137-140.
The authors note the traditional pairings of subjects i.e., math and
science, and language arts social studies. They propose an interdisciplinary
union between social science and mathematics in the middle school years.
Problem solving is the focus between the two disciplines. Problem solving in
mathematics is referred to in cited literature. Problem solving in social
studies is clearly identified as two processes: Exploration and Inquiry. Each
of these two processes is presented in a step-by-step format with the Inquiry
portion being more descriptive. A subsequent table shows the two processes
in problem solving as compared to each other and to the mathematics
approach. In the end, the teacher has the opportunity for the students to
reflect and connecting when approaching a problem in the social studies and
mathematical contexts.
Sakshaug, L. E., & Wohlhuter, K. A. (2010). Journey toward teaching
mathematics through problem solving. School Science and
Mathematics 110, (8), 397-409.
A group of teachers are learning to teach through problem solving
in a “Teaching Elementary School Mathematics” graduate course. The
course enabled 41 participant teachers to feel more comfortable in teaching
mathematics realizing the importance of group work while problem solving.
The study involved the teaching of mathematics that differed from the
teachers’ experiences in how they were taught mathematics. The teacher
participants tested their abilities to be problem solvers as well as action
researchers. Data collected involved reflections by the teachers’ success and
challenges concerning their own ability to choose and solve problems and
the implementation of the methodology with students in the classroom. The
study showed the importance of group work in student engagement and
success in mathematical problem solving.
Schettino, C. (2011/2012). Teaching geometry through problem-based
learning. The Mathematics Teacher 105 (5), 346-351.
Schettino proposed to explore a problem-based learning model for
the geometry unit upon reflection and examination of his current text- based
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unit. Reference literature on problem-solving curriculum is included in the
article. The author gives his own interpretation of problem-based learning:
“An instructional approach of curriculum and pedagogy where student
learning and content material are constructed (and co-constructed) through
the use, facilitation, and experience of contextual problems in a
decompartmentalized, threaded topic format ins a discussion-based
classroom setting where student voice, experience, and prior knowledge are
valued.” The purposeful approach by the author is evident in the article as
he articulates the reasons for the specific activities and the anecdotal data
resulting from implementation with the students. The author does state the
necessary balance between a teacher’s “…attempt to balance respectful
intervention with presentation of new material and elicitation of information
from the students.”
Shatzer, J. (2008). Picture book power: Connecting children’s literature
and mathematics. The Reading Teacher 61(8), 649-654.
Shatzer offers the elementary school teacher a starting point for
integrating literature and mathematics. The author explores and connects
math concepts into two categories with respective to literature: “Children’s
Literature With Specific Math Content” and “Children’s Literature Without
Specific Math Content”. Eating Fractions and A Chair for My Mother are two
picture books found in their respective tables showing the math concept and
possible employable strategies for teachers. Shatzer offers ideas and
strategies for each category. Teachers who find it a challenge to include
stories without specific math content will find a very good starting point in
this article in their unit planning. The article is supported by reference on
the mathematical processes. Literature cited is also included as a separate
section. The ideas and strategies offered are in response to the
interdisciplinary methodologies involving English language arts and
mathematics.
Stylianides, G. (2010). Engaging secondary students in reasoning and
proving. Mathematics Teaching 219, 39-44.
The author outlines the components required for students acquiring
reasoning and proving capabilities. The article is aimed at secondary school
teachers. A table “An analytic framework of reasoning-and-proving” is
included in the article with the following guiding question: “What are the
major activities involved in reasoning-and-proving?” The two column
headings are “Making generalizations” and “Developing arguments” with
accompanying rows: “Mathematical component”, “Learner component” and
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“Pedagogical component”. Examples accompanied by explanations were
given for each component. The model serves as a guide for teachers seeking
direction for forming questions for students, showing a “relationship
between proof and other activities.”
Westwood, P. (2008). What Teachers Need To Know About Numeracy.
Victoria, Australia: ACER Press.
This chapter book presents a comprehensive look at numeracy for
the pre-school, elementary and secondary school teachers. There is a list of
identified thematic issues at the beginning of each chapter. The thematic
issues are thoroughly expanded and supported by researched information.
There is an extensive and valuable reference section at the back of the book.
This reference book belongs in a teacher’s professional library.
Wilcox, B., & Monroe, E. E. (2011). Integrating writing and mathematics.
The Reading Teacher 64 (7), 521-529.
There are four “Pause and Ponder Questions that the authors
attempt to address in this article: “Why might we want to integrate writing
and mathematics? How can mathematics serve as a context for developing
the writing process? Why use writing as a tool for developing mathematical
thinking? How can teachers integrate writing, with or without revision, and
mathematics? The authors present six ideas for integrating writing with
mathematics at the elementary level: Writing Without Revision- Learning
Logs, Think-Write-Share, Note-Taking/Note-Making and Writing With
Revision- Shared Writing, Class Book, Alphabet Books. A student example of
each particular topic accompanies each idea: “Definitions and Examples of
Mean, Median, and Mode” and “…Probability”, “Example Showing a Clear
Understanding of Equivalent Fractions” and “Example of Equivalent
Fractions, Before and After Revision”, “Note-Taking/Note-Making: A Fifth
Grader’s Conception of Integers”, “A Shared Writing About Geometry
Composed and Revised by Third Graders and Their Teacher”, “A Class Book
Page About Word Problems Written and Illustrated by Fourth Graders”, and
“An Alphabet Book Page: ‘T Is for Transformation’ Completed by a Fifth
Grader”, respectively. The authors provide purpose, description and some
teacher and student experiences/reflections for each particular idea.
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