Bemidji State University
 M1013/ MATHEMATICAL FOUNDATIONS FOR MIDDLE SCHOOL TEACHERS (4 credits)
Spring 2015
MWF, 2-3 pm

Instructor:  Dr. Glen Richgels

Email: -- grichgels@bemidjistate.edu

Office Phone: 755- 2824

Office hours

 

 

Professional Education  Department Mission Statement:

 

 ÒThe Bemidji State University Professional Education program is preparing today's teachers for tomorrow, through effective, inquisitive, and reflective practice. Our students are proficient, self-reliant, and thoughtful practitioners, developed in a viable and growing program, who can teach effectively in various settings with diverse learners."

 

 

 

 

 

Course Description

1013 MATHEMATICS FOR ELEMENTARY SCHOOL TEACHERS II (3 credits) This course meets the BOT 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 manipulatives for modeling the basic concepts.

Prerequisites

MATH 1011 or consent of instructor.

Required Text

Mathematics for Elementary Teachers: A Contemporary Approach (2011) by G. L. Musser, W. F. Burger, & B. E. Peterson; John Wiley & Sons (pub)

Resources:

Minnesota K-12 Mathematics Framework (1998) by W. Linder-Scholer. SciMathMN (pub).  Number Sense Activities section.

Principles and Standards for School Mathematics (2000). NCTM; Reston, VA.

 



Board of Teaching Standards

8710.3200 Teachers of Elementary Education K-6

Department of Mathematics and Computer Science

 

 

 

 

8710.3200 Teachers of Elementary Education K-6

 

 

 

 

In this syllabus you will find the word TEACH. This will mean to:

  1. Launch:  This is where the teacher sets the context of the problem or activity being worked on this day.  This involves making sure the students clearly understand the mathematical context and the mathematical challenge of the dayÕs activities.
  2. Explore:  This is the time where the students get to work in pairs, individually, or as a class to solve problems presented by the lesson.
  3. Share: This occurs when most of the students have made sufficient progress toward solving the problem presented with todayÕs lesson.  It is during this phase that the students learn how others approached the problem and possible solution routes.  Helps students deepen their understanding of the mathematical ideas presented in the dayÕs lesson.
  4. Summarize:  During this phase the teacher concludes the lesson by clearly stating what the main idea was in the lesson, being sure to clear up any confusion that may arise during the ÒshareÓ segment.  Helps students focus their understanding of the mathematical ideas presented in the lesson.

 

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;

 

 

 

(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:

 

 

 

 

(a) help students investigate situations that involve counting finite sets, calculating probabilities,

KA

Chapter 11

HW 11.1, 11.2

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 interative procedures to find elements of arithmetic, geometric, and other sequences on homework, in-class work, and on questions on Test 1.

Students will analyze arithmetic, geometric, and other sequences to generate iterative procedures or rules for the 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

Geometric growth of populations

Snowplow routes, delivery routes, traveling salesman – nearest neighbor

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:

 

 

 

 

(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.

Regular polygon investigation.

Jordan Curve Theorem

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:

 

 

 

 

(a) understand the properties and relationships of geometric figures;

 

KA

Chapter 12

Van Hiele levels
Venn diagram triangles, quadrilaterals

Regulare polygon investigation

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

Perimeter, area, and volume
calculate for given figures

Students will design an original abstract measurement system and be able to list positive aspects of their system.

Students will construct a table for eight measurement concepts, English units, and System International, metric, units.

Students will be able to give examples of where the different units for measurement concepts are used in real world applications.

Students will use the relationship between volume, capacity, and mass in the SI (metric) system in homework and in-class discussions and on test 4.

 

(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

Geoboards – perimeter, area, ratios, venn diagrams

Chapter 14

Constructions – compass and straight edge, patty paper, MIRA

Surface area and volume of hemi-spheres and spheres

Tiling, regular polygons, platonic solids

Students will demonstrate how to use geoboards to illustrate perimeter, area, ratios and Venn diagrams.

Students will be able to perform standard constructions such as angle bisector, segment bisector, and perpendicular bisector using straight edge and compass, MIRA, and patty paper on homework and in-class work or on Test 5.

Students will find the surface area and volume of a sphere, cylinder, cone, prism, and pyramid on homework, in-class work, or on questions on Test 4.

Students will identify regular and semi-regular tilings of a plane and the platonic solids formed from regular polygons on homework, in-class work or on Test 3.

(5) data investigations:

 

 

 

 

(a) use a variety of conceptual and procedural tools for collecting, organizing, and reasoning about data;

 

KA

Chapter 10

Tally marks, stem and leaf plot, box and whisker plot, conclusions

Raisin Activity

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 Tendancy: Mean, median, mode

Max, min, range, IQR, quartiles, outlier

Dispersion: range, standard deviation

Bar charts, histograms, pie charts, line graphs, pictographs

For a given set of data, students will organize it and display the data using stem and leaf plots, histogram, pie chart, or appropriate graphical technique. 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 studentsÕ abilities to communicate mathematically;

KA

 

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:

 

 

 

 

(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:

 

 

 

(b) understand the connections among mathematical concepts and procedures, as well as their application to the real world;

 

KA

Chapter 12

n-gons and tiling

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;

 

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.

 

Technology Requirements and Expectations
Students may use internet browsers to access information and answer questions posed in class. Students may use graphing calculators, GeometerÕs Sketchpad, or data programs such as Excel, Tinkerplots, Fathom 2, or Minitab as needed. Written assignments for class will be composed using a word processor such as Microsoft Word.

 

 

Teaching Methodology
PolyaÕs problem solving steps

1.     Understand the problem

    1. Devise a plan
    2. Carry out the plan
    3. Reflect

 

Lesson Sequencing

                  Intuitions Þ Concrete ó Semi-Concrete ó Abstract

 

GlenÕs Teaching/Learning Principles

1.     Teach the way students learn

2.     Use group work, heterogeneous, 3-4, change monthly

3.     Communication student ó student

4.     Communication teacher ó student

5.     Multiple solution paths

6.     Use contextual settings / problem solving

7.     Assessment

    1. Grading
    2. To inform instruction

 

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
Upon request this document can be made available in alternate formats. Please contact Kathi Hagen at Disabilities Services at (218) 755-3883 for assistance or the AUC Office at 262-6753 or (800) 369-4970.

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 for those students who attend class regularly and complete assignments that they will earn an A or B.

- I am available for help whenever I am in my office. I encourage students to do homework at a table outside of my office so that I can help them whenever they have difficulties. Help is also available through email and at my home, if prior arrangements have been made.   

- I will try to give grade status reports at least every three weeks.   

 

Course Grades
A:              100 – 90%                               B:  89 – 80%                                             C:  79 – 70%                           D:  69 – 60%

Course Policies
Attendance: Daily attendance is expected
Participation: Class participation and group work is expected

Tentative Course Calendar

Week 1

Day 1

Syllabus, Assignments, Integer rules

Day 2

Integer rules; add, subtract, multiply; chip trading

Day 3

Number systems to rational numbers/decimals

Week 2

Day 4

Decimals < - > fractions base 10, n terminating

Day 5

Fractions -> decimals repeating

Day 6

Fractions -> decimals repeating

Week 3

Day 7

Repeating decimals -> fractions; .999 repeating = ?

Day 8

Decimals repeating, terminating, neither <-> rational numbers, irrational numbers

Day 9

Test 1

Week 4

Day 10

Data collection heights; why do we collect data; what is typical data

Day 11

Stem and leaf plots, line plots; mean, median, mode

Day 12

Box and whisker plots

Week 5

Day 13

Box and whisker plots

Day 14

Intuitive likely-hood statements

Day 15

Quantify probability; list, table, tree sample spaces; success counting, total counting

Week 6

Day 16

Probability assignments from experiments

Day 17

Probability conditional

Day 18

Test 2

Week 7

Day 19

Geometry definitions, parallel lines

Day 20

AmberÕs parallel lines activity

Day 21

Regular polygon properties activity

Week 8

Day 22

Regular and semi-regular tessellation of plane

Day 23

Omoinoes activity: number, perimeter, area, box and cube templates

Day 24

Jordan simple closed curve theorm; game board, three utility problems

Week 9

Day 25

Take a trip geometric perspective activities

Day 26

3D views; top, side, right perspectives

Day 27

Test 3

Week 10

Day 28

Measurement island activity

Day 29

Measurement concepts, SI small and big triangles

Day 30

Unit conversions

Week 11

Day 31

Geoboard activities, perimeter, area

Day 32

Perimeter and area formulas

Day 33

Conservation of volume; 3D solids organization activity

Week 12

Day 34

Volume and surface area problems; prisms, pyramids, cylinders, cones, sphere

Day 35

Volume and surface area problems; prisms, pyramids, cylinders, cones, sphere

Day 36

Test 4

Week 13

Day 37

Constructions ruler and compass

Day 38

Constructions Mira and patty paper; Mira activities

Day 39

Congruent triangles tool kit and activities

Week 14

Day 40

Similar triangles took kit and activities

Day 41

Transformational geometry flips, slides, turns, similitudes

Day 42

Transformational geometry flips, slides, turns, similitudes

Week 15

Day 43

Topology, euler circuits

Day 44

Test 5

Day 45

Final Exam Review

 

Day 46

Final Exam