Eastern Connecticut State University
Education Department
Methods in Elementary Mathematics (EDU 411)
Outline, Fall 2013
Instructor: Dr. Hari P. Koirala
Class hours: M, 8:30-11:15 am & Online
Office: Webb 129
Classroom: GO 102
Office hours: M, T, W, 3–6 pm; F, 9-11 am or by an appointment
Phone: 860-465–4556 (W)
Email: koiralah@easternct.edu
________________________________________________________________________
Purpose of the course
This course will be coordinated with EDU 306, EDU 412, and EDU 413. The overall goal of
this course is to encourage you to embrace the challenge of learning to teach through inquiry into
students’ understanding of mathematics and the mathematics curriculum. Although there are no
recipes and formulas for teaching mathematics, this course will provide you opportunities to explore
how students learn mathematics and how you can use various teaching approaches to engage
students into mathematical thinking.
A significant portion of this course will be spent on designing and analyzing elementary school
mathematics lessons and units. This course is built around the elementary school mathematics
content areas as outlined in the Common Core State Standards (CCSS): Operations and Algebraic
Thinking, Number and Operations in Base Ten and Fractions, The Number System, Expressions and
Equations, Measurement and Data, Geometry, and Statistics and Probability. Also integrated in this
course are the eight mathematical practices as outlined in the CCSS and the Association of
Childhood Education International (ACEI, 2007) standards and indicators required for elementary
teacher candidates. All course goals, objectives, and themes are interconnected with the Education
Unit Conceptual Framework Candidate Proficiencies (ECP), Connecticut Pre-service Teacher
Competencies (PTC), 2010 Connecticut Common Core of Teaching (CCT), the CCSS and the
NCTM and ACEI standards for mathematics. The following table shows the elements of ECP, PTC,
and CCT.
Eastern Candidate
Proficiencies (ECP)
Preservice Teacher
Competencies (PTC)
Common Core of Teaching
(CCT)
1: Content Knowledge (CNK)
2: Pedagogical Knowledge
(PDK)
3: Integration of Knowledge
(INT)
4: Technology as a Tool to Teach
(TTT)
5: Diversity (DIV)
6: Professionalism (PRF)
1: Development and
Characteristics of Learners
2: Evidence-based/Standardsbased Instruction
3: Evidence-based Classroom and
Behavior Management
4: Assessment
5: Professional Behaviors and
Responsibilities
Domain 1: Content and
Essential Skills
Domain 2: Classroom
Environment, Student
Engagement, and Commitment
to Learning
Domain 3: Planning for Active
Learning
Domain 4: Instruction for
Active Learning
Domain 5: Assessment for
Learning
Domain 6: Professional
Responsibilities and Teacher
Leadership
1
The table below provides an outline of how the goals and objectives of this course align with the
ECP, PTC, CCSS, and the ACEI standards. Also, each goal/objective is associated with a student
product that would be completed during the course.
Course Goals/Objectives/Candidate Proficiencies
Course Goals/Objectives
ECP, PTC,
and CCT
Alignment
ACEI Standards and the
CCSS
Products
By the end of the course students will:
1. Demonstrate in-depth understanding
of content knowledge including
central concepts, principles, skills,
tools of inquiry, and structure of
mathematics by using various
mathematical contents such as
number and number operations,
patterns and relationships, functions
and algebra, measurement and
geometry, and statistics and
probability in designing mathematics
lessons and units for students.
2. Use various mathematical processes
such as problem solving, reasoning,
communication, connections, and
representation in designing
mathematics lessons and units.
3. Be aware of the availability, use, and
limitations of a variety of resources
and strategies to enhance student
learning of mathematics.
4. Use technology such as computers,
calculators, and other multi-media in
the teaching of mathematics.
5. Plan, design, and implement
curriculum lessons and units in
mathematics which are consistent
with the national and state standards.
6. Use various assessment strategies
such as questioning, journals, and
portfolios to monitor student learning
and improve instruction.
7. Demonstrate an ability to support the
diverse needs of students in terms of
exceptionalities, race, ethnicity,
gender, culture, language, and
socioeconomic status.
ECP: 1.1
PTC:
CCT:
Domain 1
ACEI Standard 2.3
CCSS domains: Operations
and Algebraic Thinking,
Number and Operations in
Base Ten and Fractions,
The Number System,
Expressions and Equations,
Measurement and Data,
Geometry, and Statistics
and Probability
ECP: 1.1,
2.1, 2.2, 3.1
PTC:
CCT:
Domain 1
ECP: 2.2,
2.3
PTC: 1, 2
CCT:
Domain 2-4
ECP: 4.1
PTC: 2
CCT:
Domain 2-4
ECP: 2.12.4
PTC: 1-5
CCT:
Domain 3
ECP: 2.4
PTC: 4
CCT:
Domain 5
ECP: 5.1,
6.1
PTC: 1, 5
CCT:
Domain 6
2
Attendance,
Participation, &
Dispositions
(APD)
Philosophy
(PH)
Unit Plan (UP)
Clinical Report
& Presentation
(CR)
ACEI Standard 2.3
CCSS all domains listed
above and mathematical
practices
APD, PH, UP,
CR
ACEI Standards 1.0, 3.13.5; CCSS all domains
listed above and
mathematical practices
APD, PH, UP,
CR
ACEI Standards 1.0, 3.13.5; CCSS all domains
listed above and
mathematical practices
ACEI Standards 1.0, 2.3,
3.1-3.5, 4.0
CCSS all domains listed
above and mathematical
practices
ACEI Standard 4.0
CCSS all domains listed
above and mathematical
practices
ACEI Standards 3.2, 5.1,
5.2; CCSS all domains
listed above and
mathematical practices
APD, PH, UP,
CR
APD, PH, UP,
CR
APD, PH, UP,
CR
APD, PH, UP,
CR
Grading
Final grades in this course will be determined on total points earned out of 100 in the following
way:
95–100 A
77–79 C+
90–94 A74–76 C
87–89 B+
70–73 C-
84–86 B
65–69 D+
80–83 B60–64 D
Below 60
F
Disability Statement: If you are a student with a disability and believe you will need
accommodations for this class, it is your responsibility to contact the Office of AccessAbility
Services at (860) 465-0189. To avoid any delay in the receipt of accommodations, you should
contact the Office of AccessAbility Services as soon as possible. Please note that accommodations
are not retroactive, and that I cannot provide accommodations based upon disability until I have
received an accommodation letter from the Office of AccessAbility Services. Your cooperation is
appreciated.
Academic Services Center: Students are encouraged to use the support offered by the Academic
Services Center (ASC) located on the ground floor of the Library. Advising Services and tutoring
in math, writing, and other subjects, including supplementary instruction, are available. The ASC
also offers assistance in study techniques, time management and understanding learning styles. Fall
2013 hours: Sun. 2-9; M.-Th. 9-9, Fri. 9-5. (Closed Sat.) For further information call 465-4310 or
check the ASC website at http://www.easternct.edu/asc/.
Academic Misconduct: Students should read and understand Eastern's Academic Misconduct
Policy, which can be found in the Eastern Student Handbook or at:
http://www.easternct.edu/judicialaffairs/academicmisconduct/ All violations will be handled under
the procedures established in this policy.
Electronic communication: Effective August 1, 2009, Eastern email will become an
official form of correspondence within Connecticut State University System (CSUS).
Therefore, it is expected that communications to students sent via email will be received and
read in a timely fashion. It is expected that students check their university email at least as
often as their class meets, in recognition that certain communications may be time-critical.
Students should not assume that email sent from outside providers will be received by their
professor.
Library Research Guidelines. For library research guidelines, please go to the
Education/Curriculum Research Guide in the following website:
http://easternct.libguides.com/education
3
Course Text
Cathcart, G. W., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2011). Learning mathematics in elementary
and middle schools: A learner-centered approach (5th ed.). Boston: Pearson.
Other Course Materials
Association of Childhood Education International (ACEI, 2007). Association for Childhood Education
International Elementary Education Standards and Supporting Explanation. Retrieved from
http://www.ncate.org/LinkClick.aspx?fileticket=2G2qXsJF9cI%3d&tabid=676
Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Retrieved
from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
Connecticut State Department of Education. (2010). 2010 Common Core of Teaching: Foundational Skills.
Retrieved from http://www.sde.ct.gov/sde/lib/sde/pdf/educatorstandards/Board_Approved_CCT_2-32010.pdf
Connecticut State Department of Education. (2010). Regulation of State Board of Education, Rev. 2-3-2010,
Part III, Pre-Service Teacher Competencies. Retrieved from
http://www.sde.ct.gov/sde/lib/sde/pdf/cert/regulations/2015_proposed_regulations_11-10-2010.pdf
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics.
Reston, VA: Author. Retrieved from http://standards.nctm.org/.
National Council of Teachers of Mathematics. (2006). Curriculum focal points for prekindergarten through
grade 8 mathematics: Reston, VA: Author. Retrieved from
http://www.nctm.org/standards/default.aspx?id=58
Please note that these materials would be integrated throughout this course. There may be other readings as
assigned by the instructor.
4
Tentative Weekly Calendar
Session
Course readings/Assignments
September 2
Labor Day Holiday—No class
September 9
Course introduction; CCSS and NCTM Standards, Professional journals
Current issues in mathematics education; Constructivist view of learning
September 16
Planning lessons and units
Performance and portfolio assessment, SBAC
Text chapters 1 & 2
Draft Philosophy of Mathematics Education Due
September 23
Teaching Problem Solving and assessing student understanding
Text chapters 3 & 4
September 30
Teaching of numbers and operations
Text chapters 5, 6, 7, 8, & 9
Revised Philosophy of Mathematics Education Due
October 7
Teaching of fractions, decimals, percent, ratio, and proportion
Text chapters 10, 11, 12, & 13
Early Lesson Plan Due
October 14
Teaching of geometry and measurement
Text chapters 14 & 15
October 21
Teaching of probability and statistics
Text chapter 16
Teaching with technology (calculators and computers)
Draft Unit Plan Due
Oct 28; Nov 4
Clinical in Schools
November 11
Teaching of Algebra
Text chapter 17
November 18
Student presentations
Revised Unit Plan Due
November 25
Student presentations
December 2
Student presentations
December 9
Lesson Defense (Also on Dec. 4)
Clinical Report Due
Disposition Reflection Due
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Course Assignments*
Note that all written assignments must be submitted through Blackboard Learn.
Attendance, Participation, Dispositions, and Online Threaded Discussion [26%]
One purpose of this course is developing a community that is concerned about the teaching and learning
of mathematics. Each member of the class is essential to the development of a learning community and, as
such, regular attendance and participation is expected of all students in classroom and online.
Each student must participate in an online threaded discussion every week (See Blackboard Learn for
details). You are expected to check the course website at least two times a week to read and respond to
messages. I have posted discussion topics and directions on Blackboard. The topics are related to your
textbook and other suggested readings. In each discussion topic, you’re expected to read every message and
respond to some of them just like you would listen to everybody in a physical class and would respond to
questions and comments posed by the instructor and your peers. More specifically, you are required to
respond to every single topic/prompt provided by the instructor. In addition to your own original posting on a
topic/prompt, you must respond to at least two discussion messages posted by class members under each
topic. The postings in online discussion will weigh 17% of the course grade. Your postings will also affect
your disposition grade.
Provided below are some of the discussion topics. Please go to Blackboard Learn for more specific
directions and timeline.
1. Please read the NCTM Standards, NCTM PreK-8 Focal Points, and the Common Core State
Standards in Mathematics (CCSSM). After reading please post your comments on how these
documents will guide your mathematics education philosophy and curriculum. You may focus on
such questions: What are the major content areas in elementary school mathematics? How important
are the NCTM process standards such as mathematical problem solving and mathematical
representation? Which NCTM principle do you think is most critical in teaching elementary school
mathematics? What are some of the relationships between the NCTM process standards and the
mathematical practices delineated in the Common Core State Standards?
2. Please select a teaching strategy from Chapter 3 or Chapter 4 in your text (Cathcart et al., 2011).
Describe the strategy and its importance in elementary mathematics curriculum. How will this
strategy help elementary school students develop a conceptual understanding of mathematical
problem solving? Has your host teacher in your field experience school ever used this strategy? If
two people have already discussed a particular strategy, then you must discuss a different kind of
strategy.
3. In this TD please share your ideas about Unit Plan and get feedback from each other. You can post
any idea such as the topic and lessons you’ve chosen, an activity you have developed, or an
assessment strategy you’ve thought about. Hope this TD will help you to come up with solid ideas
about your unit plan.
4. How important is the study of fractions for elementary school children? How are fractions related to
whole numbers and rational numbers? What are some of the misconceptions children may have
about fractions? How should teachers address these misconceptions? Provide an example from your
*
All writing assignments should be typed and double spaced. At least 1 inch margin on all sides of paper is required.
Criteria for evaluating all the assignments are attached. See those criteria for details.
6
field experience classroom. Also, make sure to cite the text (Chapter 10, 11, 12, or 13) in this
discussion.
5. Many international tests have indicated that elementary school students in most other countries
outperform their U.S. peers in geometry and measurement. Explain why the U.S. students find it
difficult to understand geometry and measurement? In your explanation, cite the text (Chapters 14
and 15) and any article you may find it in a journal or from an online source. How should teachers
address this problem?
6. Based on your experience of working with students and course readings, discuss the profile of a
student(s) with special needs (exceptionalities, race, ethnicity, gender, culture, language, and/or
socioeconomic status). What kinds of challenges or opportunities arise because of these needs during
math lessons? What specific kinds of strategies would you use to support their math learning? If two
people have already discussed a particular need, then you must discuss a different kind of needs.
7. This is the final threaded discussion in this course. Over the semester, you were engaged in a variety
of activities in mathematics education. Please think for a moment and reflect on what you learned in
this course. What concepts and/or activities were most important for you? Why? How would you use
these concepts/activities in your teaching? Note that your answers may vary from one another.
Dispositions Assessment
At the end of this course, you must submit a 1-2 page reflection describing your strengths and challenges
with respect to target or acceptable dispositions as explained in the rubric. Grades will be determined by
carefully comparing your reflection with my notes. Although you will write your disposition reflection at the
end of the course, you will have opportunities to demonstrate required dispositions throughout this course. If
needed, meetings will be conducted with individual student(s) to discuss how dispositions can be improved.
Dispositions Rubric
Target (3)
Acceptable (2)
Unacceptable (1)
Class
participation
Attended every class, always
came on time, submitted all
assignments by their due dates,
was not distracted, and was
actively engaged in online as well
as on-campus group and whole
class activities.
Missed more than one
class, often came late,
and/or was inactive or
distracted in group/whole
class activities. Did not
actively participate in
online discussions
Professionalism
Read professional and research
journal(s) in their discipline(s) to
improve their own personal and
professional growth, sought
membership of professional
organization(s) to become
involved in the professional
community of educators, and
demonstrated passion and
enthusiasm for their discipline(s)
and methods of teaching.
Missed one class or
discussion, almost always
came on time or only
partially participated in
online discussions,
submitted all assignments
by their due dates, was not
distracted, and was actively
engaged in online and oncampus activities.
Read professional and
research journal(s) in their
discipline(s) and
demonstrated some passion
and enthusiasm for their
discipline(s) and methods of
teaching.
7
Did not read professional
and research journal(s) in
their discipline(s) and/or
did not demonstrate
passion and enthusiasm
for their discipline(s) and
methods of teaching.
Respect
Displayed professional and
ethical behavior in all class
activities, always paid attention
and listened to peers and the
instructor of the class with
respect, and often responded
thoughtfully and appropriately to
the ideas of peers and the
instructor.
Displayed professional and
ethical behavior in all class
activities, and always paid
attention and listened to
peers and the instructor of
the class with respect.
Did not display
professional and ethical
behavior in all class
activities and/or did not
pay attention to the ideas
of peers and the instructor
of the class.
Philosophy of Mathematics Education (9%)
Write a one-page statement of your philosophy of mathematics education. Specifically write
your goals of mathematics teaching and the roles of students and teachers in the learning of
mathematics. You have to first submit a draft of your philosophy for the instructor's feedback. In the
final version of your philosophy you must address all questions/concerns raised by the instructor.
PHILOSOPHY RUBRIC
Logic and
clarity
Connections
to classrooms
Readings,
citations, and
formatting
Target (3)
The philosophy statements are
direct, straightforward, and
unambiguous. The paper
consists of well defined and
clearly developed paragraphs
which are consistent and
logically connected to each other
maintaining the flow of the
paper. It is well focused.
The statements are supported by
meaningful examples and
illustrations from classroom
and/or personal experiences.
The philosophy statements are
based on critical reflection of
course readings. The paper
follows proper APA formatting
consistently.
Acceptable (2)
The philosophy statements are
generally clear but sometimes
ambiguous. The paper
consists of clearly developed
paragraphs which are logically
connected to each other
maintaining the flow of the
paper. It is focused.
Unacceptable (1)
The philosophy statements
are unclear and ambiguous.
The paper does not consist
of well defined and clearly
developed paragraphs. It
does not maintain the flow
of the paper. It is not
focused.
The statements are supported
by examples from classroom
and/or personal experiences.
The statements are not
supported by examples from
classroom and/or personal
experiences.
The philosophy statements
are not based on reflection
of course readings. The
paper does not follow
proper APA formatting.
The philosophy statements are
based on reflection of course
readings. The paper follows
APA formatting.
Early Lesson Plan (5%)
You are required to submit this lesson plan using the Eastern’s lesson plan template used in prestudent and student teaching. The template is provided on Blackboard Learn. The assignment
criteria and rubric for this lesson plan will be the same used for lesson planning in your unit (your
next assignment). The primary purpose of this assignment is to provide you with feedback so that
you’re more likely to successful in your unit planning.
Overview and Design of a Unit [30%]
This is a very important assignment that students must complete in this course. This assignment will consist
of several elements. Its main purpose is to help candidates develop a unit of mathematics that could be used
in their teaching. The candidates are required to develop outlines of at least 10 lessons, three of which must
be full lesson plans using the Eastern lesson plan format used during student teaching. There will be one
lesson plan in each grade band K-2, 3-4, and 5-6. Because the candidates have to develop a unit that
8
shows how mathematical contents are interconnected and extended across grade levels, they need to
consider the skills and abilities of the students in a particular grade level before choosing and/or
planning lessons. The unit will include:

A concept map;

A unifying theme and assumptions for the unit;

A list of the resources, including technology;

Statements of how the unit aligns with some of the state and national standards (CCSS and NCTM);

Citation and analysis of at least five sources/articles, including the CCSS and NCTM standards, related
to the unit;

Objectives of the unit;

Outline of at least 10 lessons;

Three fully developed lesson plans using Eastern’s lesson plan template (used during student teaching);

A tentative timeline, showing a possible sequence of unit topics and the amount of time allotted to each
topic;

An account of how and where this unit might fit with other mathematical content areas;

An account of how this unit might fit with other subject areas;

An outline of how instructional tools and mathematics-specific technology are integrated in the unit;



A description of how the unit shows the importance of mathematics in everyday life and real-world
contexts;
A description of how the unit will provide students with problem solving and modeling opportunity and
enhance their problem solving skills;
Ways of assessing students’ understanding of mathematics (both formative and summative).
At least two of following mathematics topics from the CCSS should be covered in the unit:

Operations and algebraic thinking (Operations, whole numbers, integers, patterns)

Number and Operations in Base Ten (Place value whole numbers and decimals)

Number and Operations-Fractions (fractions)

The Number System (multi-digit numbers, fractions and rational)

Expressions and Equations (expressions, equations, inequalities, algebraic equivalence etc.)



Measurement and Data (length, time, liquid, money, perimeter, area, volume, and representing and
interpreting data)
Geometry (Lines, angles, classification/properties of shapes both 2D and 3D, coordinates)
Statistics and Probability (statistical variability and distributions) and Probability (Games, concepts,
rules, combinatorics etc.)
9
The design of a unit should be based on the principle that “the whole is more than the sum of its parts.” That
is to say a unit plan is more than a collection of lesson plans. You are encouraged to work in small groups of
2-3 people to bounce off ideas. However, you have to submit your own individual unit. The unit plan will be
evaluated based on the attached rubric.
Unit Plan Rubric
Themes, timelines,
assumptions,
concept map, and
unit objectives
ACEI, 2007, 1.0
Quality of lesson
plans
ACEI, 2007, 3.1
Assessment
strategies
ACEI, 2007, 4.0
Mathematical
content knowledge
and processes
ACEI, 2007, 2.3
Target (3)
The unit contains a clear
description of unified theme,
the grade level, topic, a
tentative timeline, entry-level
characteristics, features,
resources to be used, concept
map, and objectives that are
clear and adequate.
Acceptable (2)
The unit contains a clear
description of unified theme,
the grade level, topic, a
tentative timeline, entry-level
characteristics, features,
resources to be used, concept
map, and objectives, some of
which may not be clear or
adequate.
The lesson plans include all the
components: topics, grade
level, connection to the
standards, objectives,
procedures, assessment
strategies, and differentiation
and accommodation plan. The
lesson plans focus on student
engagement and mathematical
understanding.
The unit contains sufficient
number of assessment strategies
(both formative and
summative) and some sample
quizzes, exams, projects, and
alternative assessment
techniques. Each assessment
includes a rubric or grading
criteria.
The unit demonstrates that the
candidate has a thorough
knowledge of assessments used
by some of the leading
assessment organizations in the
state and the nation (e.g. SBAC
and NAEP).
Shows understanding of
content, by providing
appropriate examples from at
least two CCSS content areas
mentioned above, (e.g.
operations and algebraic
thinking, measurement/data).
The unit is fully supported by
specific mathematics concepts
and questions. Errors are not
made.
The lesson plans include at
least six components: topics,
grade level, connection to the
standards, objectives,
procedures, assessment
strategies, and differentiation
and accommodation plan.
The lesson plans focus on
student mathematical
understanding.
The unit contains adequate
number of assessment
strategies (both formative and
summative) and some sample
quizzes, exams, projects, and
alternative assessment
techniques. Some
assessments include rubric or
grading criteria.
The unit demonstrates that
the candidate has knowledge
of assessments used by some
of the leading assessment
organizations (e.g. SBAC
and NAEP).
10
Shows understanding of
content, by providing
appropriate examples from at
least two CCSS content areas
mentioned above (e.g.
operations and algebraic
thinking, measurement/data).
The unit is supported by
specific math concepts and
questions. Errors are rarely
made.
Unacceptable (1)
The unit lacks a clear
description of unified
theme, the grade level,
topic, a tentative timeline,
entry-level
characteristics, features,
resources to be used, and
objectives, many of
which are not clear or
adequate.
The lessons miss two or
more components or do
not focus on student
mathematical
understanding.
The unit does not contain
adequate number of
assessment strategies or
no rubric or grading
criteria is provided.
The unit does not
demonstrate that the
candidate has knowledge
of assessments used by
some of the leading
assessment organizations
(e.g. SBAC and NAEP).
Lacks understanding of
mathematical content.
Examples are not
provided or they lack
comprehension. Errors
are made.
Does not demonstrate
understanding of
mathematical practices
described in the CCSS.
Mathematical
modeling and
problem solving
ACEI, 2007, 3.3
Lessons
connection
ACEI, 2007, 3.1
Dealing with
diverse learners
ACEI, 2007, 3.2
Use of
Manipulatives &
Technology
ACEI, 2007, 3.5
Use of Research
ACEI, 2007, 3.1
Organization and
Presentation
Also demonstrates full
understanding of mathematical
practices described in the
CCSS.
There is at least one problem in
the unit plan which provides a
solid mathematical problem
(based on modeling), at least
two ways of solving it, and an
excellent description of how the
problem can be used to teach
elementary school mathematics.
Fully demonstrates how the
lessons in the unit are
interconnected and how the unit
is connected to other content
areas, everyday life, and the
real-world.
The unit provides a clear
description of how it can be
extended to serve high or low
ability students. Some
activities are modified for this
purpose. Students' special
needs are clearly identified.
Uses technology as a tool for
modification.
Thoroughly describes how
instructional tools such as
manipulative and physical
models, virtual manipulatives,
and mathematics- specific
technology such as calculators,
spreadsheets, and interactive
software packages (e.g.
Geogebra) enhance the teaching
of mathematics content in this
unit.
Shows appropriate citation and
analysis of research (including
ones from professional
mathematics education
organizations such as the
NCTM’s print, digital, and
virtual resources/collections)
related to the unit that leads
students in rich mathematical
learning experiences.
The unit plan is well organized
and is free of spelling and
grammatical errors.
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Also demonstrates
understanding of
mathematical practices
described in the CCSS.
There is at least one problem
in the unit plan which
provides a mathematical
problem (based on
modeling), at least one way
of solving it, and a
description of how the
problem can be used to teach
elementary school
mathematics.
Demonstrates how the
lessons in the unit are
interconnected and how the
unit is connected to other
content areas, everyday life,
and the real-world.
The unit provides a
reasonably adequate
description of how it can be
extended to serve high or low
ability students. Some
activities are modified for
this purpose. Students'
special needs are identified.
Uses technology as a tool for
modification.
Describes how instructional
tools such as manipulative
and physical models, virtual
manipulatives, and
mathematics- specific
technology such as
calculators, spreadsheets, and
interactive software packages
enhance the teaching of
mathematics content in this
unit.
Shows appropriate citation
and analysis of research
(including ones from
professional mathematics
education organizations such
as the NCTM’s print, digital,
and virtual
resources/collections) related
to the unit that leads students
in mathematical learning
experiences.
The unit plan is organized. It
may have some minor
spelling and grammatical
errors.
The problem selected is
not based on
mathematical modeling or
the description of using it
at the elementary level is
unclear.
Does not demonstrate
how the lessons in the
unit are interconnected or
how the unit is connected
to other content areas.
No clear description of
how the unit can be
extended to serve high or
low ability students.
Students' special needs
are not identified. Does
not use technology as a
tool for modification.
Does not describe how
instructional tools
enhance the teaching of
mathematics content in
this unit.
Does not show
appropriate citation and
analysis of research
related to the unit that
leads students in
mathematical learning
experiences.
The unit plan is not
organized or has many
spelling and grammatical
errors.
Note: Incomprehensible and missing responses will result in a score of 0.
Investigating Students’ Understanding of Mathematics (Clinical Report) [30%]
This assignment is directly related to your clinical experience in an elementary classroom. While in
school, you are expected to investigate students’ understanding of mathematics. You can accomplish this
task by implementing the following steps:
Design a pre-test and post-test to assess students’ mathematical content you will be teaching in
your clinical classroom. Administer the pre-test prior to teaching your lesson.
ii)
Teach a mathematics classroom and take careful notes related to the following questions: What
was the mathematical content and what national and common core state standards did this fit
into? What kinds of manipulatives or other teaching resources were used by you (the teacher)
and students? What kinds of teaching/learning strategies were used? Who was more engaged;
students or the teacher? How frequently did the students ask questions? Was this primarily a
traditional/behaviorist or a progressive/constructivist classroom?
iii)
Administer the post-test after teaching your lesson. This will help you to decide whether or not
your teaching made a positive impact on student learning.
iv)
Select two students (one at a higher mathematical level and one at a lower mathematical level)
based on your pre- and post-tests and also with coordination from your clinical experience
teacher and interview them to investigate their mathematical understanding. Collect student
work and take interview notes. If it is hard to take notes during the interview you can tape
record the interviews and transcribe them later in your convenience.
v)
Analyze pretest, posttest, and other student work and determine their understanding of
mathematics. Do you think that these students achieved the lesson objectives? If so, what is the
evidence? If not, what went wrong?
Write a report. In your report you must cite at least eight readings, including both the CCSS and NCTM
standards. You also need to provide a reference page using the APA formatting. Your report must
include the following:
i) Describe the context and mathematical levels of students that you taught. Describe the lesson
(content and standards).
ii) Discuss the pretest, posttest, problem and interview questions that you asked the two students.
iii) Analyze student work and interviews and report your findings. Discuss with evidence whether or
not the lesson objectives were met.
iv) Finally provide your reflection on how you would change the lesson to better suit the students’
needs.
v) Attach your lesson plan, pre- and post-tests, and some work samples from the two students you
selected.
i)
Your report should be no more than 10 pages in length (double-spaced), excluding the attachments.
You will also need to give a 10 minute presentation to the EDU 411 class about your lesson. Your
oral presentation in class should include the following steps:
a) Bring the manipulatives/resources used in the school classroom. If no resources were used, you
must prepare similar manipulatives/resources to demonstrate to the class during your
presentation.
b) Describe the lesson (content and standards) you observed and the mathematical levels of
students (1-2 minutes).
c) Carry out a portion of the lesson in EDU 411 class, including an activity with the
manipulatives/resources that you bring to the class (5-6 minutes). During your activity make
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sure that EDU 411 class is engaged. Your job is not to lecture what you did but to engage the
class in a meaningful way.
d) Ask a question and lead the discussion (1-2 minutes). Make sure that the question is related to
the topic of your presentation.
Clinical Report and Presentation Rubric
Classroom and
interview context
ACEI, 2007, 3.1
Lesson Plan
ACEI, 2007, 3.2
Analysis of
teaching, student
work and
interviews
ACEI, 2007, 3.4
Monitoring and
Adjusting
ACEI, 2007, 4.0
Comparison of
analysis to course
readings and
research
ACEI, 2007, 5.1
Target (3)
The description of student
background, classroom
context, and lesson presented
to the students is clear and
coherent.
The lesson plan used for
teaching clearly demonstrates
how the teacher candidate
planned to differentiate
mathematics content for
diverse groups of students
and how mathematicsspecific instructional tools
were used in building all
students’ conceptual
understanding and procedural
fluency.
The analysis of teaching,
student work, and interviews
is clear, meaningful, and
insightful.
The analysis demonstrates
that the teacher candidate
created learning environment
in which students were
actively engaged in building
new knowledge from prior
knowledge and experiences.
The teacher candidate
effectively uses formative
and summative assessments
(pre-test/post-test) to measure
students’ understanding of
mathematics, monitors
students’ progress, and
makes instructional decisions
to help students develop
conceptual understanding and
procedural fluency.
The analysis is compared to
course readings including the
PTC, CCT, CCSS and
NCTM standards in a
meaningful way (at least 5
citations).
The analysis clearly indicates
that the candidate utilized
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Acceptable (2)
The description of student
background, classroom
context, and lesson presented
to the students is generally
clear.
The lesson plan used for
teaching indicates how the
teacher candidate planned to
differentiate mathematics
content for diverse groups of
students and how
mathematics-specific
instructional tools were used
in building students’
conceptual understanding and
procedural fluency.
Unacceptable (1)
The description of student
background, classroom
context, and lesson
presented to the students is
unclear.
The lesson plan used for
teaching does not indicate
how the teacher candidate
planned to differentiate
mathematics content or how
mathematics-specific
instructional tools were
used in building students’
conceptual understanding
and procedural fluency.
The analysis of teaching,
student work, and interviews
is clear.
The analysis demonstrates
that the teacher candidate
created learning environment
in which students were
engaged in building new
knowledge from prior
knowledge and experiences.
The analysis of teaching,
student work, and
interviews is unclear or a
component is missing.
The analysis does not
demonstrate that the teacher
candidate created an active
learning environment.
The teacher candidate uses
formative and summative
assessments (pre-test/posttest) to measure students’
understanding of
mathematics, monitors
students’ progress, and
makes instructional
decisions.
The teacher candidate does
not use formative and
summative assessments or
does not make effective
instructional decisions.
The analysis is compared to
course readings or the PTC,
CCT, CCSS and NCTM
standards.
The analysis indicates that
the candidate utilized
resources from professional
mathematics education
The analysis is not
compared to course
readings or the standards.
The analysis does not
indicate that the candidate
utilized resources from
professional mathematics
education organization.
Impact on student
learning
ACEI, 2007, 4.0
Use of
Manipulatives &
Technology
ACEI, 2007, 1.0
Activity and
engagement in
presentation
Reflection
ACEI, 2007, 5.1
Organization and
Presentation
resources from professional
mathematics education
organization
organization.
The analysis and reflection
clearly indicate that the
teacher (candidate) is making
a highly positive impact on
student learning.
Appropriate grade level
manipulatives and
technology are used in the
EDU 411 class presentation.
The students in EDU 411
class are actively engaged in
class activities.
The analysis and reflection
provide some indication that
the teacher (candidate) is
making a positive impact on
student learning.
Appropriate grade level
manipulatives or technology
is used in the EDU 411 class
presentation
The students in EDU 411
class are engaged in class
activities.
The analysis and reflection
do not indicate that the
teacher (candidate) is
making a positive impact on
student learning.
Appropriate grade level
manipulatives or technology
is not used in the EDU 411
class presentation.
The students in EDU 411
class are not engaged in
class activities.
Reflection is focused on
lesson objectives and it
clearly articulates future
directions on how the lesson
should be changed. The
reflection is meaningful and
compared with the standard
documents including the
preservice teacher
competencies (PTC) and the
Common Core of Teaching
(CCT).
The clinical report is well
organized and is free of
spelling and grammatical
errors.
Reflection is focused on
lesson objectives and it
provides future directions on
how the lesson should be
changed. The reflection is
compared with the standard
documents including the
preservice teacher
competencies (PTC) and the
Common Core of Teaching
(CCT).
Reflection is not focused on
lesson objectives, does not
provide future directions, or
is not compared with the
PTC or CCT. Sometimes
these elements may be
unclear.
The clinical report is
organized. It may have some
minor spelling and
grammatical errors.
The clinical report is not
organized or has many
spelling and grammatical
errors.
Note: Incomprehensible and missing responses will result in a score of 0.
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EASTERN CONNECTICUT STATE UNIVERSITY EDUCATION UNIT CONCEPTUAL FRAMEWORK
Candidate Proficiencies for ECSU Candidates
1: Content Knowledge (CNK)
1.1 Candidates/Graduates demonstrate in-depth understanding of content knowledge including central concepts,
principles, skills, tools of inquiry, and structure of the discipline(s) by engaging students through meaningful
questions and learning experiences.
2: Pedagogical Knowledge (PDK)
2.1 Candidates/Graduates are able to formulate developmentally appropriate learning goals and objectives for
students based upon knowledge of subject matter, students, the community, curriculum goals (both state and
national), and theories of human development, and to plan and implement instructional activities which foster
individual and collective inquiry, critical thinking, and problem solving to facilitate learning for all students
in a safe and nurturing environment.
2.2 Candidates/Graduates use methods, activities, and grouping arrangements appropriate for lesson goals and
objectives in an environment that is conducive to learning.
2.3 Candidates/Graduates conduct learning activities in a logical sequence and respond to the developmental
needs, interests, ability, and background of students to promote their development of critical thinking,
independent problem-solving, and collaborative inquiry.
2.4 Candidates/Graduates use multiple forms of assessment to evaluate student learning and modify instruction
as appropriate to ensure the continuous intellectual, social, ethical, and physical development of the learner.
3: Integration of Knowledge (INT)
3.1. Candidates/Graduates demonstrate how different concepts, themes, and principles are interconnected within
and across the discipline(s) and promote connections between content knowledge and pedagogical
knowledge to help students learn concepts, principles, skills, tools of inquiry, and structure of the
discipline(s) they teach.
3.2. Candidates/Graduates demonstrate an ability to integrate learning theories and other pedagogical knowledge
in their clinical experiences and student teaching.
4: Technology as a Tool to Teach (TTT)
4.1. Candidates/Graduates integrate appropriate digital and non-digital technology throughout their courses and
clinical experiences to support student learning.
5: Diversity (DIV)
5.1. Candidates/Graduates demonstrate their ability to support the diverse needs of students in terms of
exceptionalities, race, ethnicity, gender, culture, and socioeconomic status.
6: Professionalism (PRF)
6.1. Candidates/Graduates collaborate with cooperating teachers, other teachers, school administrators and other
school professionals, parents, families, and communities in a professional and ethical manner to help
students reach their maximum potential.
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