Teacher Education Program Mission Statement:
BSU prepares teachers through inquisitive, involved, reflective practice. The framework outlining our program sets a standard that is rigorous, exemplary and innovative. The curricular structure is research based and organized around the Standards of Effective Practice. Graduates are proficient, collaborative, technologically literate and environmentally aware teachers, who work effectively in various settings with diverse learners.
Math 1013
Math for Elementary Teachers II
Instructor: Todd Frauenholtz
Office: 372 HS
Phone: 755-2817
Email: TFrauenholtz@BemidjiState.edu
Website: http://faculty.bemidjistate.edu/tfrauenholtz
Class meets: M, W, F in DH 113 from 9:00 - 9:50 am.
Office hours: M, W, F from 10:00 - 10:50 am in TRIO and by other arrangement.
Text: Reconceptualizing Mathematics for Elementary Teachers , third ed. by Sowder, Sower, & & Nickerson
WebAssign at: https://www.webassign.net/ Class Key: bemidjistate 9521 7497
Description: This course meets the new Professional Education Licensing and Standards Board's introduction to higher mathematics competencies. These topics include geometry, discrete mathematics, probability, and statistics. This is the second of two mathematics courses providing the background for teaching in the elementary school. Emphasizes the use of mathematics manipulative for modeling the basic concepts. Prerequisite: Math 1011 or equivalent.
The topics addressed include mathematics found in elementary curricula. Including:
Goals and objectives of the course:
Competencies to be met by law.
Homework: Homework assignments will be made in class. You should read and understand all sections of the chapters and assigned problems to prepare for quizzes and exams. Points will be given for homework.
Class participation and quizzes: Class participation is expected and in order to participate you need to be present. Quizzes will be unannounced and given frequently to help you prepare for the exams. Quizzes cannot be made up but your lowest quiz score will be dropped from the calculation of your grade. Cell phones must be turned off during class.
Exams: There are five exams planned in addition to the comprehensive final exam. Make-up exams will be given only under special circumstances and need to be discussed with me before hand. The final exam is scheduled for Tuesday, May 5th from 8:00 - 10:00 am.
Grades: Grades for this course will be based upon homework, quizzes, tests, and a comprehensive final exam; some of the quizzes may be unannounced. Items for both will come from the assigned homework. The following grading scale will be used to determine grades:
A | 90 – 100 % |
B | 80 – 89 % |
C | 70 – 79 % |
D | 60 – 69 % |
F | Below 60% |
Make-ups are not allowed for missed quizzes, instead I will
allow you to drop your lowest quiz score from the term.
All tests will count toward your final grade.
The instructor reserves the right to adjust the grading scale if
necessary.
Working through the assigned problems is essential to
learning mathematics. Showing your
work is the only way to receive partial credit and hence is very important.
Academic integrity:
Students are expected to practice the highest standards of ethics,
honesty, and integrity in all of their academic work.
Any form of academic dishonesty (e.g., plagiarism, cheating,
misrepresentation) may result in disciplinary action. Possible disciplinary actions may include failure for part or
all of a course, as well as suspension from the University.
I would like to make sure that all the materials, discussions and activities that are part of the course are accessible to you. If you would like to request accommodations or other services, please contact me as soon as possible. It is also possible to contact Accessibility Services, Decker Hall, 202. Phone: 218/755-3883 or E-mail address Accessibilityservices@bemidjistate.edu. Also available through the Minnesota Relay Service at 1-800-627-3529.
Daily Course Outline
Day 1 |
Introductions & explore algebra tiles & I Spy paterns (NCTM 3-5 Navigations Through Algebra) |
Day 2 |
What's my rule, looking at patterns |
Day 3 |
Arithmetic and Geometric Sequences |
Day 4 |
Graphs to stories and Stories to Graphs
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Day 5 |
Interpretting graphs |
Day 6 |
Building Houses and practice problems from LaunchPad
Gayle has $30,000 salary and 2.4% commission while Helena has a $25,000 salary and 4% commission. Who has the better compensation package? |
Day 7 |
K-2 Navigations: Math Machines, How Does it Grow?, Number Roads, Block Pounds, Balancing Act, and I Spy Patterns. 3-5 Navigations: The Ups & Downs of Patterns, Squares Cubed, Triangle Rule Machine, and Algebra Scales
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Day 8 |
Test 1 |
Day 9 |
Review Test 1 and begin geometry. Finding central, interior, and exterior angles of regular polygons. |
Day 10 |
Geometry terms and finding missing angles
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Day 11 |
Venn Diagrams of quadrilaterals and triangles
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Day 12 |
Polyhedra: Faces, Vertices, and Edges of Relational Geo-solids. Are they related?
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Day 13 |
Isometric dot paper and perspective drawings
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Day 14 |
Nets to make polyhedra
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Day 15 |
Tetrominoes spinner & cover up board
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Day 16 |
Alphabet Symmetry
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Day 17 |
Box Puzzle and tessellations
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Day 18 |
Tangrams -- make the seven squares
Reflections of Images & Using Scale Factors (NCTM - Navigations Through Geometry 6-8) |
Day 19 |
Isometric Explorations & Isodot Paper More Tangrams -- looking at side length and area of the seven squares
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Day 20 |
Review for Test 2
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Day 21 |
Test 2
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Day 22 |
Euclidean constructions
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Day 23 |
Proving the Euclidean constructions worked!
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Day 24 |
Geometric topics |
Day 25 |
Reflection of Image and Scale Factor (NCTM Navigations Through Geometry 6-8)
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Day 26 |
Translations, Rotations, and Reflections
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Day 27 |
Measurement with non-standard units |
Day 28 |
Finding lengths and area on Geoboard |
Day 29 |
Compare volume of prism and pyramid – arrange
geo-solids by volume |
Day 30 |
Calculate surface area and volumes of geo-solids |
Day 31 |
Metric and standard measurements – metric time? |
Day 32 |
Building formulas – A = b h and V = 1/3 B h |
Day 33 |
Using formulas on a test.
Tennis ball problem (missing area/volume) |
Day 34 |
Test 3
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Day 35 |
Introducing probability as a number between zero and one
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Day 36 |
Tree diagrams, area model, list, and tables to represent probability
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Day 37 |
Dr. Todd presenting at NCTM
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Day 38 |
With replacement or without replacement
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Day 39 |
Solving similar triangles |
Day 40 |
Euclidean constructions |
Day 41 |
Translations and rotations |
Day 42 |
Topological equivalency |
Day 43 |
Test 5 |
Day 44 |
Review for Final exam
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Technology Requirements and Expectations
Students will use internet browsers to access information and answer questions posed in class. Students may use graphing calculators, Geometer’s Sketchpad, or data programs such as Excel, Tinkerplots, Fathom 2, or Minitab as needed. Written assignments for class may be composed using a word processor such as Microsoft Word.
Teaching Methodology
Polya’s problem solving steps
Lesson Sequencing
Intuitions Þ Concrete Û Semi-Concrete Û Abstract
Glen’s Teaching/Learning Principles (adopted by Dr. Frauenholtz)
University Policies and Procedures
http://www.bemidjistate.edu/students/handbook/policies/
Academic Integrity
BSU students are expected to practice the highest standards of ethics, honesty and integrity in all of their academic work. Any form of academic dishonesty (e.g., plagiarism, cheating and misrepresentation) may result in disciplinary action. Possible disciplinary actions may include failure for part of all of a course as well as suspension from the University.
Students with Special Needs
I would like to make sure that all the materials, discussions and activities that are part of the course are accessible to you. If you would like to request accommodations or other services, please contact me as soon as possible. It is also possible to contact Disability Services, Sanford Hall, 201. Phone: 218/755-3883 or E-mail address Disabilityservices@bemidjistate.edu. Also available through the Minnesota Relay Service at 1-800-627-3529.
Student Rights and Responsibilities
Student Code of Ethics
http://www.bemidjistate.edu/academics/catalog/10catalog/GradCatalog/Frontpages/sectionIV/rights.html
Student Academic Rights and Responsibilities
http://www.bemidjistate.edu/students/handbook/policies/academic_integrity/rights_responsibilities.cfm
Instructor Rights and Responsibilities
- I work with all students and expect success from all students. It is my expectation that those students who attend class regularly and complete assignments will succeed in my class.
- I am available for help whenever I am in my office in addition to my office hours. I encourage students to do homework in groups, and discuss the homework problems thoroughly so they can explain their reasoning in class.
- I can be reached via email outside of class time.
Course Grades
A: 100 – 90% B: 89 – 80% C: 79 – 70% D: 69 – 60%
Course Policies
Attendance: Daily attendance is expected. Makeup exams are provided only in emergency situations. Quizzes missed cannot be made up.
Participation: Class participation and group work are expected.
STANDARDS OF EFFECTIVE PRACTICE FOR TEACHERS
Department of Mathematics and Computer Science
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8710.3200 Teachers of Elementary Education K-6 |
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In this syllabus you will find the word TEACH. This will mean to:
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Standard |
K/A |
Activity |
Assessment |
H. A teacher of children in kindergarten through grade 6 must demonstrate knowledge of fundamental concepts of mathematics and the connections between them. The teacher must know and apply; |
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(2) concepts and techniques of discrete mathematics and how to use them to solve problems from areas including graph theory, combinatorics, and recursion and know how to: |
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(a) help students investigate situations that involve counting finite sets, calculating probabilities, |
KA |
Chapter 11 |
Students will demonstrate their ability to count finite sets with the counting principle, table diagram, or tree diagram as they build sample space models for events on homework, in-class work, and on questions on Test 3. Students will demonstrate their ability to calculate probabilities for simple and compound events on homework, in-class work, and on questions on Test 3. |
tracing paths in network graphs, |
KA |
Euler circuits and paths |
Students will demonstrate the understanding of tracing of network graphs by classifying the graphs as Euler circuits, Euler paths, or neither on homework, in-class work, and on questions on Test 5. |
and analyzing iterative procedures; and |
KA |
Arithmetic and geometric sequences |
Students will use iterative procedures to find elements of arithmetic, geometric, and other sequences on homework, in-class work, and on questions on Test 1. |
(b) apply these ideas and methods in settings as diverse as the mathematics of finance, population dynamics, and optimal planning; |
KA |
Finance – compound interest |
Students will apply iterative procedures in diverse settings of mathematics such as finance, to calculate compound interest, population dynamics to find populations from one generation to the next, or in optimal planning for snowplow routes, delivery routes, and guided tours on homework, in-class work, or on questions on Test 1 and 5. |
(3) concepts of numerical literacy: |
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(d) understand the relationships of integers and their properties that can be explored and generalized to other mathematical domains; |
KA |
Operations and properties of integers. Evens/Odds in probability. |
Students will demonstrate that they understand the relationships of integers and their properties that can be explored and generalized to other mathematical domains such as probability, graph theory, and geometry on homework and in-class work. |
(4) concepts of space and shape: |
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(a) understand the properties and relationships of geometric figures; |
KA |
Chapter 12 |
Students will demonstrate and understanding of the relationships of geometric figures when they construct a Venn diagram for seven classifications of triangles or a Venn diagram for nine classifications of quadrilaterals. |
(b) understand geometry and measurement from both abstract and concrete perspectives and identify real world applications; and |
KA |
Chapter 13 |
Students will design an original abstract measurement system and be able to list positive aspects of their system. |
(c) know how to use geometric learning tools such as geoboards, compass and straight edge, ruler and protractor, patty paper, reflection tools, spheres, and platonic solids; |
KA |
Chapter 9,13 |
Students will demonstrate how to use geoboards to illustrate perimeter, area, ratios and Venn diagrams. |
(5) data investigations: |
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(a) use a variety of conceptual and procedural tools for collecting, organizing, and reasoning about data; |
KA |
Chapter 10 |
Students will collect data on the heights of individuals in cm, organize the data using tally marks and stem and leaf diagrams, and box plots. Students will draw at least one conclusion from the constructed box plot and give it orally when asked in class. |
(b) apply numerical and graphical techniques for representing and summarizing data; |
KA |
Central Tendency: Mean, median, mode |
For a given set of data, students will organize it and display the data using stem and leaf plots, histograms, pie charts, or appropriate graphical techniques. The students will find the measures of center, mean, median, mode, measures of dispersion and variation maximum, minimum, range, inter-quartile range (IQR), quartiles and outliers for given data sets on homework, in-class work, and on questions on Test 2. |
(c) interpret and draw inferences from data and make decisions in a wide range of applied problem situations; and |
KA |
Use measures of dispersion to identify typical and atypical data |
Students will interpret and draw inferences from data and make decisions in a wide range of applied problem situations on homework, in-class work, or on questions on Test 2. |
(d) help students understand quantitative and qualitative approaches to answering questions and |
KA |
Analysis of qualitative and quantitative data |
Students will choose quantitative or qualitative approaches to answer data questions posed in class. |
develop students’ abilities to communicate mathematically; |
KA |
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Students will receive feedback on their notation and mathematical symbolism as they communicate between themselves or to the teacher on homework, in-class work, and on questions on all tests. |
(6) concepts of randomness and uncertainty: |
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(a) probability as a way of describing chance in simple and compound events; and |
KA |
Define probability of events and calculate probability of simple and compound events |
Students will model sample spaces for simple and compound events and will calculate the desired probabilities from these sample spaces on homework, in-class work, and on questions on Test 2. |
(b) the role of randomness and sampling in experimental studies; |
KA |
Sampling as a representation of a population |
Students will be able to describe how to gather data from a large population to answer questions in experimental studies on homework and in-class work. |
(7) mathematical processes: |
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(b) understand the connections among mathematical concepts and procedures, as well as their application to the real world; |
KA |
Chapter 12 |
Students will construct a table to investigate the connections between mathematical concepts procedures of regular polygons in order to answer questions relating to regular, semi-regular, and non-regular tiling of planar surfaces on homework and in-class work. |
(c) understand the relationship between mathematics and other fields; |
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Data and probability |
Students will describe how to use data and probability to answer questions of interest in other academic areas and applied areas in real life in class discussion. |
updated 1/24/2020
by Todd
Frauenholtz