Mathematical Concepts for Elementary Education II
Section 1 MWF 1:30-2:20p
Telephone: 5403 (245-5403)
Office Hours: Monday 11:30a - 12:20p, Wednesday
4-5p, Thursday 1-2p, 8-9p, Friday 2:30 - 3:30p, and by
appointment or visit.
Elementary School Teachers Explorations, and Mathematics for Elementary School Teachers
by Tom Bassarear
Occasional additional handouts provided
Required Supplementary Materials
Manipulative Kit, Scissors
Course Goals and Philosophy
The purpose of this course is to revisit the content
of the elementary mathematics curriculum with the focus on
understanding the underlying concepts and justifying the solutions of
problems dealing with this material. The focus is not on being able to
perform the computations (the how to do it), although that is a
necessity as well, but on demonstrating an ability to explain
why you can solve the problem that way or why the
algorithm works that way. You will need to be able communicate your
both verbally and in writing with strict attention to the mathematical
accuracy and clarity of your explanation. You will have the chance
to work with mathematical concepts in an active, exploratory manner
as recommended by the National Council of Teachers of Mathematics
Knowing mathematics means being able to use it in
To learn mathematics, students must be engaged in exploring,
conjecturing, and thinking rather than only rote learning of rules and
procedures. Mathematics learning is not a spectator sport. When
students construct knowledge derived from meaningful experiences, they
are much more likely to retain and use what they have learned. This
fact underlies the teacher's new role in providing experiences that
help students make sense of
mathematics, to view and use it as a tool for reasoning and problem
If you feel a need to review elementary school
mathematics, this is your responsibility. For this purpose, I
recommend reading our textbook and consulting with me outside of
class. For a reference on the content of elementary school
mathematics, here are the common core state standards
It is also the purpose of this
course to improve your ability to engage in mathematical thinking
and reasoning, to increase your ability to use mathematical knowledge
to solve problems, and to learn mathematics through problem
The emphasis in this course is on learning numerical mathematical
concepts through solving problems. You will often work with other
students for the following reasons: Group problem solving is
broader, more creative, and more insightful than individual
While working on problems with others, students practice putting their
mathematical ideas and reasoning into words. This ability to
mathematics is clearly essential for future teachers. While
in groups, students learn to depend on themselves and each other
than the instructor) for problem solutions. In groups, students
motivate each other to excel and accept more challenging
problems. Motivation to persevere with a difficult problem may be
Socialization skills are developed and practiced. Students are
exposed to a variety of thinking and problem-solving styles different
own. Interaction with others may stimulate additional insights
discoveries. Conceptual understanding is deeper and
longer-lasting when ideas are shared and discussed.
Your grade in this course will
be based upon your performance on problem sets, weekly questions,
reflection logs, three exams, and the final project. The
assigned to each is designated on the left in the grade definition
scale given on the right:
10% - Participation
A 90 - 100
10% - Weekly
B 80 - 89.99
20% - Each of two
70 - 79.99
15% - Final
D 60 - 69.99
25% - Comprehensive
0 - 59.99
You are preparing to enter a profession where good
attendance is crucial and expected. It is important that you make
every attempt to attend class, since active involvement is an integral
of this course. Since much of the class is experiential, deriving
same benefits by merely examining someone's class notes or reading the
textbook would be impossible. Each class period you will be
working on activities with your group. If you are working in your
group you will receive
one participation point that day. If you also participate to the
class as a whole (answer a question, present a solution, ask an
insightful question or offer important relevant commentary) you will
receive two participation points for that day. If you are not
working in your group, you will receive no points for that day.
Working each day and never speaking in class will earn 80%.
Speaking every other day on which there is
an opportunity to speak will earn 95%. Scores between will be
On Wednesdays, I will assign a question relating to
the topic for the previous week. They will be due approximately
once a month as indicated on the schedule. The goal of these
assignments is for you to write substantial explanations of the main
concepts presented in class. They will eventually be incorporated
into your final project. Before the final project, they will be
collected for completeness and marked with suggestions.
Assignments are due at the start of class and must be easy to read.
Late assignments will not be accepted.
These questions and papers will be graded on the
(out of 2)
0 – missing question
1 – question attempted, but
2 – question addressed
and in depth
In order to provide you with extensive comments,
there may be delays in returning these papers.
Two in-class exams will be given. Their focus is
largely conceptual and problem solving based. You should be able to explain the concepts behind any
calculations, algorithms, etc. Material will come from lectures,
discussions in class, and the text. For example, you will need to be
able to explain clearly and with mathematical accuracy why we
can solve problems in certain ways or why various algorithms
or procedures work mathematically. You will also need to be able to use
and explain the use of the manipulatives relevant to the material.
In-class exams will take two days - the first day
devoted to a group exam, in which your group will complete an activity
much like those done in-class. You will submit one well-written
presentation of your findings from each group.
Individual exams will contain six questions: four of
the questions will be direct problems. Two of
the questions will be more open ended and ask you to explain key
concepts from class. The exams will be graded as follows:
you will receive 40 points for attempting the exam. You may earn
up to 10 points on each of the questions.
Make-ups for exams will be given only in extreme
cases with arrangements made with the instructor prior to
the exam or if there is a verifiable medical excuse or permission from
the Dean of Students. If you miss an exam and we have not made
arrangements prior to the missed exam, you must contact me before the
This project will be a collection of
weekly question items that you will write up throughout the semester.
could one day be included in your professional portfolio to demonstrate
your level of mathematical understanding and preparation and your
ability to communicate mathematics in a clear and correct manner.
A complete, organised, well-presented compilation of all
materials is due on the last day of class. Your project will be
checked for inclusion of all assigned topics and will be evaluated
based on the clarity and accuracy of the explanations given as well as
the overall presentation (neat, easy to find sections and entries, easy
to read, well-written, & c). Somewhere in this portfolio you
must demonstrate appropriate uses of each of the manipulatives
used in class.
Occasionally you will be given
anonymous feedback forms. Please use them to share any thoughts
or concerns for how the course is running. Remember, the sooner
you tell me your concerns, the more I can do about them. I have
also created a web-site
which accepts anonymous comments.
If we have not yet discussed this in class, please encourage me to
create a class code. This site may also be accessed via our course
page on a link entitled anonymous
course, you are always welcome to approach me outside of class to
discuss these issues as well.
This center is located in South Hall
332 and is open during the day and some evenings. Hours for the center
will be announced in class. The Math Learning Center provides free
tutoring on a walk-in basis.
While working on homework with one another is
encouraged, all individual write-ups of solutions must be your own. You are
expected to be able to explain any solution you give me if asked.
Exams will be done individually unless otherwise directed.
Student Academic Dishonesty Policy and Procedures will be followed
should incidents of academic dishonesty occur.
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning
disabilities. Students should consult with the Director in the
Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin,
firstname.lastname@example.org) and their individual faculty regarding any needed
accommodations as early as possible in the semester.
It is my policy to give students who miss class
because of observance of religious holidays the
opportunity to make up missed work. You are responsible for
me no later than September 12 of plans to observe a holiday.
This is a course in the mathematics
department. This is your mathematics content course. In
this course, you will develop a mathematical background necessary in
order to teach elementary school students. You will deepen your
understanding of gradeschool mathematics topics and connections.
You will not be learning how to teach mathematics to children, that is
the purpose of
your methods course in the school of education. As a
mathematician, I am trained to teach you mathematics, and I will do
that. I am not trained to teach you how to educate, and that is
not the goal of this course. Please keep this in mind.
We will be undertaking a great
amount of interactive group work in this course. You may
view these as games. If you come in eager to play, then you
will be more likely to be successful and perhaps occasionally enjoy
the games. If you come in saying "I don't want to play this
game," we will all be annoyed and frustrated, and the course as a whole
will be less successful. Please play nicely.
Out of necessity, I am more formal in class and more
personal out of class. If you ever want
additional help, please come to see me either during my office hours,
at an appointed time, or by just stopping by (I am frequently in my
office aside from the times that I will certainly be there). It
is important that you seek help when you start needing it, rather than
when you have reached desperation. Please be responsible.
Teaching is one profession where you have direct
impact on hundreds of lives. It is truly
an incredible responsibility. It is vitally important that
teachers set high expectations for themselves and their students.
Daily preparation of interesting, instructive lessons for twenty-five
or more active children of varying aptitudes is extremely
I am dedicated to helping you prepare for this exciting career, and
will try to help you reach your full potential. Best wishes for a
challenging and fulfilling semester.
Schedule (This schedule is subject to change, but I
hope to hold mostly to this outline.) Two numbers separated by a
period refer to explorations that we will be studying that day in
August 29 Introduction
8.10 WQ due
October 3 exam
9.4 WQ due
31 10.12 WQ due
November 2 10.15
21 7.3 WQ due
December 2 overflow
5 7.15 WQ due
12 Review, Final Project Due
Friday, December 16 12N - 3p
Upon successful completion of Math 141 - Math Concepts for Elementary Education II a student will be able to:
Probability and Statistics
• Design and implement a simulation to estimate experimental probability
• Calculate probabilities experimentally and theoretically.
• Recognize which events are equally likely and
which are not and calculate probabilities based on this knowledge.
• Recognize events that are mutually exclusive
and those that are not and calculate probabilities based on this
• Use complementary events to solve probability problems
• Use probability to solve problems and make decisions.
• Model multistage experiments using tree diagrams
• Model and compare experiments with and without replacements
• Recognize and use dependent and independent events to solve probability problems.
• Use geometric probability to solve problems
• Create simulations to analyze problems in which experimentation is impossible or impractical.
• Develop interesting and relevant probability
experiments and games for children of varying abilities and backgrounds.
• Use odds and expected value to solve problems and made education decisions.
• Explain the connection between probability and odds.
• Differentiate between permutations and combinations and solve problems using this knowledge.
• Solve permutations and combination problems involving like objects.
• Distinguish between and interpret pictographs,
line plots, stem-and-leaf plots, histograms, bar graphs, circle graphs,
box-and-whisker plots, and scatter-plots
• Create stem-and-leaf plots, box-and-whisker plots and circle graphs
• Compute mean, median, and mode and evaluate their usefulness in given circumstances.
• Find outliers, range, and quartiles, variance, and standard deviation
• Interpret standard deviation tables
• Calculate how addition of data changes the mean
• Evaluate how outliers effect mean
• Evaluate abuses of statistics with regard to data collection and displays
Geometry and Measurement
• Name the undefined terms of points, lines, and
planes that are basic to geometry and state their properties.
• Model, illustrate, and symbolize geometric terms and concepts
• Differentiate between plane and solid geometry.
• Use paper folding and construction tools to
explore geometric properties of lines, angles, and polygons.
• Use geoboards and other manipulatives to explore geometric concepts
• Make conjectures based on observations and explorations and justify, prove, or defend the conjecture.
• Recognize the difference between a justification and a proof.
• Classify polygons according to their properties.
• Explain the difference between measuring tools and construction tools.
• Differentiate among acute, right, obtuse, and straight angles.
• Compare and contrast polygons to create a hierarchy.
• Use organized lists and sketches to ensure
that all possible cases have been accounted for using the given in a
• Demonstrate, model, and illustrate geometric concepts for beginning learners.
• Prove theorems and conjectures for more advanced learners.
• Explore definitions and properties of
perpendicular and parallel lines and use the knowledge to solve
• Verify that the sum of the measures of the
interior angles of a triangle applies to all triangles whether they are
acute, right or obtuse.
• Prove that the sum of the measures of the
interior angles of a triangle is 180 and that the sum of the interior
angles of a convex polygon having n sides is (n-2)*180.
• Prove that the sum of the measures of the
exterior angles (one at each vertex) of a convex polygon is 360.
• Using modeling rather than memorization to
determine the sum of the measures of the interior angles of a convex
polygon with n sides.
• Solve problems that require combinations of geometric concepts.
• Visualize three dimensions figures in order to
count the number of faces, vertices, edges, and diagonals associated
with these figures.
• Define and differentiate between regular polygons and solids and those that are not regular.
• Use knowledge of nets to determine
characteristics of the unseen sides of a cube given a net of the cube.
• Model nets for solids other than cubes.
• Sketch and use networks to solve problems.
• Recognize congruence and apply the knowledge to solve problems.
• Verify that triangles are congruent using s.a.s., a.s.a., s.s.s
• Verify that a.a.a is not sufficient to prove triangles congruent
• Use construction tools to perform elementary constructions.
• Use constructions to illustrate triangle congruences and similarities
• Use a Mira and paper folding for constructions
• Verify the Pythagorean theorem using construction and scissors
• Recognize the converse of a theorem
• Use the Pythagorean theorem and its converse
• Find surface areas of geometric solids
• Find volumes of geometric solids
• Verify the conversion factor between Centigrade and Fahrenheit
• Perform translations, reflections, and rotations by constructions, using dot paper and tracing paper
• Perform compositions of transformations
• Perform size transformations
• Analyze figures to determine symmetries
• Tessellate a page using a combination of transformations
• Discover properties of altitudes and medians of triangles.
• Prove or verify that constructions actually accomplish the required outcomes
• Discover and list properties of quadrilaterals
• Discover, list, and use properties of similar triangles
• Separate a line segment into n congruent parts by construction and by using lined paper
• Use the Cartesian coordinate system to determine slopes of lines
• Use the factor/label method for measurement conversions
• Use dot paper to find areas
• understand measurable attributes of objects
• identify the units, systems, and processes of measurement
• apply appropriate techniques, tools, and formulas to determine measurements
• Use indirect measurement to solve problems
• Justify area formulas for triangles, parallelograms, and trapezoids
• Find areas of regular polygons