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Minor Curriculum Proposal
Modification to MEDU 2010
Professor Andrew Douglas
Department of Mathematics
Contents
Curriculum modification proposal form
Description and rationale of proposed changes to MEDU 2010
Chancellor’s Report Form for changes to MEDU 2010
Modified syllabus for MEDU 2010
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4
6
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New York City College of Technology, CUNY
CURRICULUM MODIFICATION PROPOSAL FORM
Title of Proposal
Date
Major or Minor
Proposer’s Name
Department
Date of Departmental
Meeting in which proposal
was approved
Department Chair Name
Department Chair Signature
and Date
Academic Dean Name
Academic Dean Signature and
Date
Modification to MEDU 2010
January 10, 2014
Minor
Andrew Douglas
Mathematics
2/6/14
Henry Africk
2/18/2014
Karl Botchway
2/24/14
Brief Description of Proposal
(Describe the modifications
contained within this proposal
in a succinct summary. More
detailed content will be
provided in the proposal body.
Brief Rationale for Proposal
(Provide a concise summary of
why this proposed change is
important to the department.
More detailed content will be
provided in the proposal body).
We propose to modify the title, description, and the
learning outcomes of MEDU 2010.
We propose to adjust the primary focus of the course
from mathematical applications to the effective use of
technology in the mathematics classroom. Previously,
technology had a secondary role in MEDU 2010.
Applications of mathematics receive considerable
attention in the BSc in Mathematics Education: One of
the components of the program is devoted to
applications of mathematics. However, technologies
most relevant to future mathematics teachers receive
much less consideration, and some important
technologies are not covered at all.
The proposed changes are consistent with CAEP
accreditation standards, CCSM standards, the NCTM
technology principle, and the curriculum of other strong
mathematics education programs.
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Proposal History
(Please provide history of this
proposal: is this a
resubmission? An updated
version? This may most easily
be expressed as a list).
2014-03-05
Passed Department Curriculum Committee: 1/30/14
Passed Department: 2/6/14
Sent the College Council Curriculum Committee:
2/26/14
ALL PROPOSAL CHECK LIST
Completed CURRICULUM MODIFICATION FORM including:

Brief description of proposal
X

Rationale for proposal
X

Date of department meeting approving the modification
X

Chair’s Signature
X

Dean’s Signature
X
Evidence of consultation with affected departments
List of the programs that use this course as required or elective, and courses that
use this as a prerequisite.
Documentation of Advisory Commission views (if applicable).
NA
X
NA
Completed Chancellor’s Report Form.
X
EXISTING PROGRAM MODIFICATION PROPOSALS
Documentation indicating core curriculum requirements have been met for new
programs/options or program changes.
NA
Detailed rationale for each modification (this includes minor modifications)
NA
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Description and Rationale of Proposed Changes to MEDU 2010
Description of Proposed Changes to MEDU 2010
The proposed changes to MEDU 2010 are described in the following table.
Current MEDU 2010
Course Title
Proposed MEDU 2010
Course Title
Pedagogy of Mathematics Applications and
Technology
Description
Technology in Mathematics Education
Students explore a wide variety of teaching and
learning strategies used in mathematics. These
strategies include oral and written
communication, quantitative literacy, soft
competencies, collaborative learning, critical
thinking, library research and use of technology.
Students will also explore theories of teaching
and learning processes and motivation.
Strategies to address students’ learning
difficulties in mathematics will be developed
based on emotional intelligence, learning styles
and other theories. Active learning through the
arts of observing, listening and questioning will
be explored. Teacher candidates will examine
ways in which students’ previous knowledge can
be used to stimulate intellectual curiosity.
Students examine the rationale and
pedagogy for the effective use of technology
in the middle and high school mathematics
classrooms. The technologies considered
may include graphing calculators, computer
algebra systems, spreadsheets, and dynamic
geometry software.
Learning Outcomes
Learning Outcomes
Upon successful completion of the course,
students should be able to:
Upon successful completion of the course,
students should be able to:
1. Evaluate and develop model lessons
that are enriched with mathematics
applications and are consistent with
state curriculum requirements and
NCTM standards.
2. Demonstrate effective pedagogical
approaches for teaching
mathematics applications.
3. Develop activities that incorporate
collaborative work and writing in
the application of mathematics to
problems in science, social science,
business, engineering, and
technology.
4. Use appropriate technology in the
solution of problems involving
mathematics applications.
Description
1. Solve a wide range of mathematical
problems using technology,
2. Use technology to assist in making
and testing conjectures,
3. Prove mathematical theorems with
technology,
4. Create mathematics lesson plans,
consistent with the CCSSM standards
and the NCTM technology principle,
that effectively incorporate
technology,
5. Describe research results related to
the effective use of technology in the
mathematics classroom.
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Rationale for Proposed Changes to MEDU 2010
We propose to adjust the primary focus of the course from mathematical applications to the
effective use of technology in the mathematics classroom. Previously, technology had a
secondary role in MEDU 2010.
Applications of mathematics receive considerable attention in the BSc in Mathematics
Education: One of the components of the program is devoted to applications of
mathematics. However, technologies most relevant to future mathematics teachers receive
much less consideration, and some important technologies are not covered at all.
The proposed changes are consistent with CAEP accreditation standards, CCSM standards,
the NCTM technology principle, and the curriculum of other strong mathematics education
programs.
Common Core State Standards in Mathematics (CCSM) and Technology
The CCSM standards require students to use technology throughout the middle school and
high school years. For instance, the CCSM standards require students to examine properties
of functions using a graphing calculator or computer algebra system; interpret data
generated by technology; and perform complex computations with technology.
National Council of Teachers of Mathematics (NCTM) Technology Principle
The technology principle of the NCTM emphasizes the importance of technology in
mathematics education:
“Technology is essential in teaching and learning mathematics; it influences the
mathematics that is taught and enhances students’ learning…Electronic technologies—
calculators and computers—are essential tools for teaching, learning and doing
mathematics.”
Technology and the Curriculum of Mathematics Education Programs
Many strong mathematics education programs include a course focused on the effective use
of technology. For instance, NYU includes MTHED 1044 Educational Technology in
Secondary School Mathematics in their mathematics education program; Stony Brook’s
masters program in mathematics education includes MAT 517 Calculators and Computers
for Teachers; and Rutgers University’s program has MED 15:254:548 Technology in
Mathematics Teaching.
Council for the Accreditation of Educator Preparation (CAEP) Standards and Technology
CAEP requires that education programs are consistent with state curriculum, and standards
of relevant professional associations, which in the case of math is the NCTM.
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Chancellor’s Report From
Section AV: Changes in Existing Courses
AV.1. Department Name: Mathematics
Existing Course Number and Course Title: MEDU 2010 Pedagogy of Mathematics
Applications and Technology
From:
Course Title
Description
Pedagogy of Mathematics
Applications and Technology
Students explore a wide variety
of teaching and learning
strategies used in mathematics.
These strategies include oral
and written communication,
quantitative literacy, soft
competencies, collaborative
learning, critical thinking,
library research and use of
technology. Students will also
explore theories of teaching and
learning processes and
motivation. Strategies to
address students’ learning
difficulties in mathematics will
be developed based on
emotional intelligence, learning
styles and other theories. Active
learning through the arts of
observing, listening and
questioning will be explored.
Teacher candidates will
examine ways in which
students’ previous knowledge
can be used to stimulate
intellectual curiosity.
To:
Course Title
Description
Technology in Mathematics
Education
Students examine the
rationale and pedagogy for
the effective use of
technology in the middle
and high school
mathematics classrooms.
The technologies
considered may include
graphing calculators,
computer algebra systems,
spreadsheets, and dynamic
geometry software.
Rationale: We propose to adjust the primary focus of the course from mathematical
applications to the effective use of technology in the mathematics classroom. Previously,
technology had a secondary role in MEDU 2010.
Applications of mathematics receive considerable attention in the BSc in Mathematics
Education: One of the components of the program is devoted to applications of
mathematics. However, technologies most relevant to future mathematics teachers receive
much less consideration, and some important technologies are not covered at all.
The proposed changes are consistent with CAEP accreditation standards, CCSM standards,
the NCTM technology principle, and the curriculum of other strong mathematics education
programs.
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Modified Course Syllabus for MEDU 2010
New York City College of Technology
The City University of New York
DEPARTMENT: Mathematics
PREPARED BY: Professor Andrew Douglas
COURSE: MEDU 2010
TITLE: Technology in Mathematics Education
DESCRIPTION: Students examine the rationale and pedagogy for the effective use of
technology in the middle and high school mathematics classrooms. The technologies
considered may include graphing calculators, computer algebra systems, spreadsheets, and
dynamic geometry software.
CREDIT HOURS: 1 cl hrs, 2 lab hrs, 2 cr
PREREQUISITES: MEDU 1021; and MAT 1475
TEXTS:
[1] Kenneth Goldberg, “Using Technology for Problem Solving in Middle and High
School Mathematics: Investigations Using Scientific and Graphing Calculators,
Spreadsheets, and The Geometer's Sketchpad,” Pearson, 2007.
ADDITIONAL INSTRUCTIONAL RESOURCES:
[2] “Exploring Geometry with The Geometer’s Sketchpad,” Key Curriculum Press, 2012.
Note: The copyright allows the instructor to photocopy worksheets for students from
this text. Students do not need to buy this textbook.
REQUIRED SOFTWARE AND HARDWARE: Geometer’s Sketchpad, Maple, graphing
calculator.
LEARNING OUTCOMES: Upon successful completion of the course, students should be able
to:
1. Solve a wide range of mathematical problems using technology,
2. Use technology to assist in making and testing conjectures,
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3. Prove mathematical theorems with technology,
4. Create mathematics lesson plans, consistent with the CCSSM standards and NCTM
technology principle, that effectively incorporate technology,
5. Describe research results related to the effective use of technology in the
mathematics classroom.
INSTRUCTIONAL OBJECTIVES
For successful completion of the course,
students should be able to:
Solve a wide range of mathematical problems
using technology,
Use technology to assist in making and testing
conjectures,
Use technology to assist in making and testing
conjectures
Prove mathematical theorems with
technology
Create mathematics lesson plans, consistent
with the CCSSM standards and NCTM
technology principle, that effectively
incorporate technology
Describe research results related to the
effective use of technology in the
mathematics classroom.
GENERAL EDUCATION LEARNING
OUTCOMES
Gather, interpret, evaluate, and apply
information discerningly from a variety of
sources.
Understand and employ both quantitative and
qualitative analysis to solve problems.
Employ scientific reasoning and logical
thinking.
Acquire tools for lifelong learning.
Work with teams. Build consensus and use
creativity.
Use creativity to solve problems.
ASSESSMENT












Student created lesson plans
Student presentations
Student guided, in-class lessons
Final exam
In class discussions
Assignments
Student guided, in-class lessons
Final Exam
Assignments, group work, final
exam.
Assignments, group work, final
exam.
Student created lesson plans
Student guided, in-class lessons
Final exam



In class discussions
Assignments
Final exam

ASSESSMENT
Classroom discussion, writing assignments,
student presentations, tests, exams.
Classroom discussion, writing assignments,
student presentations, tests, exams.
Classroom discussion, writing assignments,
student presentations, tests, exams.
Classroom discussion, writing assignments,
student presentations, tests, exams.
Classroom discussion, writing assignments,
student presentations, tests, exams.
Assignments, group work.
GRADING PROCEDURE:
 Student created lesson plans
 Student guided, in-class lesson s
 Final exam
 Class participation
 Mathematical and Pedagogical Assignments
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
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Portfolios
TEACHING AND LEARNING METHODS:
 Guided discussion
 Guided problem solving/discovery
 Group work
 Student guided lessons
WEEKLY COURSE OUTLINE:
SESSION
TOPIC
TEXT/SECTION
INTRODUCTION
1
[1]/Introduction
 NCTM standards and technology
 CCSM and technology
UNIT I. GRAPHING CALCULATORS
2
The formula for the sum of an infinite geometric series
[1]/5
3
A visual inspection of the real roots of a polynomial function
[1]/9
4
The relationship between the coefficients of a first of second
[1]/10
degree function and the behavior of its graph
5
A visual discovery of trigonometric identities
[1]/11
6
Exponential growth and exponential regression
[1]/15
7
Exploring derivatives using algebraic and visual
[1]/12
representations (Optional)
8
Research results on the classroom use of the graphing
[1]/Part II Intro.
calculator
UNIT II. DYNAMIC GEOMETRY SOFTWAR: GEOMETER’S SKETCHPAD
9
[1]/Part III Intro.
 Research results and the effective classroom use of
Geometer’s Sketchpad.
 Review of writing lesson plans.
 Review of Bloom’s Taxonomy.
10
Relating the properties of quadrilaterals to the properties of
[1]/17
their diagonals and creating a book of shapes
11
Inscribed quadrilaterals
[1]/3.18
12
The sum of the perpendicular distances from an interior
[1]/3.19
point of a regular polygon to its sides
13
The Pythagorean Theorem
[2]
14
The Law of Cosines
[2]
15
The Law of Sines
[2]
16
Triangle Congruence
[2]
17
Triangle Similarity
[2]
UNIT III. COMPUTER ALGEBRA SYSTEMS: MAPLE (Optional)
18-19
Lecture notes
 Introduction to Maple.
 Solving systems of equations graphically and
algebraically.
20
Mathematical visualization, animation, and programming in
Lecture notes
Maple
UNIT IV. SPREADSHEETS
21
Examining the trajectory of an object in motion using graphs
[1]/8
and tables of values
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23
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Recursively defined functions and the limit of an infinite
sequence
Converging and diverging infinite series and special
mathematical constants
STUDENT LESSONS AND EXAM
Student lessons/presentations
Review and final exam
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[1]/3
[1]/13
Version: January 2014
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