Bemidji State University
 Mx065/ MATHEMATICAL FOUNDATIONS FOR MIDDLE SCHOOL TEACHERS (4 credits)
Summer 2013
MTWRF, 12-4:30 pm

Instructor:  Adam Smieja, Katie Smieja

Email: -- Adam Smieja <asmieja@lfalls.k12.mn.us>; Katie Smieja <katiesmieja@gmail.com>

Office Phone:

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

MATHEMATICAL FOUNDATIONS FOR MIDDLE SCHOOL TEACHERS (4 credits)

This course meets or helps meet the new BOT rule with respect to concepts of patterns, relations, and functions; discrete mathematics; probability; and statistics that are pertinent to middle school mathematics.

Prerequisites
MATH 1011 or consent of instructor.

Required Text

No required text.

Resources:

Algebra in the Early Grades (2008) by J. J. Kaput, D. W. Carraher, & M. L. Blanton. Lawrence Erlbaum Associates; New York (pub).

Curriculum and Evaluation Standards for School Mathematics, Addenda Series Grades 5-8: Patterns and Functions (1991) by E. Phillips. National Council of Teachers of Mathematics; Reston, Virginia (pub).

Hands On Equations (1996) by H. Borenson.  Borenson and Associates; Allentown, PA (pub).

Mathematics for Elementary Teachers: A Contemporary Approach (2011) by G. L. Musser, W. F. Burger, & B. E. Peterson; John Wiley & Sons (pub), 9th ed.

Mathematics In Context: Comparing Quantities (2006) by T. A. Romberg.  Encyclopedia Britannica (pub).

Mathematics In Context: Building Formulas (2003) by T. A. Romberg.  Holt, Rinehart, and Winston (pub).

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

Navigating through Algebra in Grades 3-5 (2005) by G. J. Cuevas & K. Yeatts. National Council of Teachers of Mathematics; Reston, Virginia (pub).

Navigating through Algebra in Grades 6-8 (2007) by S. Friel, S. Rachlin, & D. Doyle with C. Nygard, D. Pugalee, & M. Ellis. National Council of Teachers of Mathematics; Reston, Virginia (pub).

Patterns and Functions Activities for Teachers by T. Frauenholtz, C. Rypkema; Bemidji State University.

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

 



Board of Teaching Standards

8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS.

Department of Mathematics and Computer Science

 

 

 

 

8710.3320 MIDDLE LEVEL ENDORSEMENT LICENSE FOR TEACHERS OF MATHEMATICS

 

 

 

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

C.A teacher with a middle level endorsement for teaching mathematics in grades 5 through 8 must demonstrate knowledge of fundamental concepts of mathematics and the connections among them. The teacher must know and apply:

 

 

 

(1)  concepts of patterns, relations, and functions:

 

 

 

(a) recognize, describe, and generalize patterns and build mathematical models to describe situations, solve problems, and make predictions;

K A

TEACH:

Problem solving

Understand the problem

Devise a plan

Carry out the plan

Revisit the problem

Examine different contextual problem situations, look for patterns, build models (tables, graphs, equations) for the patterns, generalize the patterns, solve the problem for the solution or extend the pattern to predict the solution. Encourage multiple approaches or solution paths.

 

Assignment:

Week: 1, 2, 6

PaulÕs points – from SciMathMN Frameworks Number Sense Activities

 

The School Store – from Math In Context Comparing Quantities.

 

Functions and Relations – from Musser, Burger, & Peterson; Section 9.3, #Õs: 2,3,6,7,8.

 

 

Assessment:

-       During class students will give presentations of models/patterns they constructed and the class will be expected to generalize patterns and make predictions.

-       On a test students will recognize, describe, and generalize patterns and build mathematical models to describe situations, solve problems, and make predictions using tables, iterative functions, and explicit functions.

 

(b) analyze the interaction within and among quantities and variables to model patterns of change and use appropriate representations, including tables, graphs, matrices, words, ordered pairs, algebraic expressions, and equations;

K A

TEACH:

Problem solving

Understand the problem

Devise a plan

Carry out the plan

Revisit the problem

Examine different contextual problem situations, look for patterns, build models (tables, matrices, words, graphs, algebraic expressions, equations) for the patterns, generalize the patterns, solve the problem for the solution or extend the pattern to predict the solution. Encourage multiple approaches or solution paths.

 

Assignment:

Week: 1, 2, 3, 4, 5, 9, 10, 11, 12, 13

Candy Boxes problem – from Algebra in the Early Grades, pp. 238-242;

 

Building Houses problem – from Navigations through Algebra in Grades 3-5;

 

Growing letters – Patterns and Function Activities for Teachers

 

Exploring Houses; Bouncing Tennis Balls; & Tiling Tubs – from Navigations through Algebra in Grades 6-8.

 

 

Assessment:

-       Students will analyze the interaction within and among quantities and variables to model patterns of change and use appropriate representations, including tables, graphs, matrices, words, ordered pairs, algebraic expressions, and iterative and explicit equations as they explain their answers orally and on a written test.

 

(c)  represent and solve problem situations that involve variable quantities and be able to use appropriate technology;

K A

TEACH:

Problem solving

Understand the problem

Devise a plan

Carry out the plan

Revisit the problem

Examine different contextual problem situations that involve variable quantities, look for patterns, build models (tables, matrices, words, graphs, algebraic expressions, equations) for the patterns, generalize the patterns, solve the problem for the solution or extend the pattern to predict the solution. Encourage multiple approaches or solution paths. Utilize technology when appropriate.

 

Assignment:

Week: 1, 2, 6, 7, 10, 11

Beams – from Math In Context Building Formulas;

 

Hands On Equations (1996) by H. Borenson.  Borenson and Associates, Allentown, PA (pub).

 

 

Assessment:

-       Students will represent and solve problem situations that involve variable quantities and be able to use appropriate technology, manipulatives, graphing calculators, or computers, as they make oral presentations explaining their approaches and solution strategies.

 

(d)  understand patterns present in number systems and apply these patterns to further investigations;

K A

TEACH:

Problem solving

á       Understand the problem

á       Devise a plan

á       Carry out the plan

á       Revisit the problem

Examine different contextual problem situations that contain patterns present in number systems, build models (tables, matrices, words, graphs, algebraic expressions, equations) for the patterns, generalize the patterns, solve the problem for the solution or extend the pattern to predict the solution. Encourage multiple approaches or solution paths.

 

Assignment:

Week: 1, 2, 5

n-gon numbers – from Addenda Series Grades 5-8: Patterns and Functions (pg. 53);

 

n-gon numbers – from Algebra in the Concrete (1973) by M. Laycock & R. A. Schadler; Activities Resource Company (pub).  Pp. 7.

 

 

Assessment:

-       Students will demonstrate they understand patterns present in number systems and apply these patterns to further investigations as they make oral presentations explaining their approaches and solution strategies and on a written exam

 

8710.4600 Teachers of Mathematics

 

 

 

Subp. 3.  Subject matter standard.  A candidate for licensure as a teacher of mathematics must complete a preparation program under subpart 2, item C, that must include the candidate's demonstration of the knowledge and skills in items A to J.

 

 

 

G.  A teacher of mathematics is able to reason mathematically, solve problems mathematically, and communicate in mathematics effectively at different levels of formality and knows the connections among mathematical concepts and procedures as well as their application to the real world.  The teacher of mathematics must be able to: 

 

 

 

(1) solve problems in mathematics by: 

 

 

 

(a) formulating and posing problems;

 

 

 

(b) solving problems using different strategies, verifying and interpreting results, and generalizing the solution;

 

 

 

(c) using problem solving approaches to investigate and understand mathematics; and

 

 

 

(d) applying mathematical modeling to real world situations;

 

 

 

 

Technology Requirements and Expectations
Students will use internet browsers to access information and answer questions posed in class. Students will 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

 

Glen RichgelsÕs 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

Introductions and 88 problem : partition into 2:3 or 3:4

Continue introductions and wrap-up 88 problem. Examine Juicy Juice problem and student work.

Look at Juicy Juice solutions and view IMAP video #3

Week 2

Wrap-up solutions to problem solving -- look at Cryptarithms / Ninebl.sol

LYNNE + LOOKS = SLEEPY ; USA + USSR = PEACE ;

Introduce variables (candy boxes) and patterns

Week 3

Growing letters – presentations

Growing letters – presentations

Growing letters – presentations

Week 4

Growing letters – presentations

Growing letters – analysis

Growing letters – analysis

Week 5

More patterns -- number of arms in classroom, growing letters, ... What is algebra? (NCTM: concrete / pictoral representation, graph, formula, table, and words)

Multiple representations on single page (from NW Service coop website)

Examine recursive (Next = Now...) and explicit (y=ax+...) formulae

n-gons – sides, vertices, diagonals from a vertex, diagonals in n-gon, central angle, interior angle, exterior angle, triangular decomposition, sum of angles – n  = 3 .. 12 ,  get formulae for N from number patterns and geometric reasoning

Week 6

PaulÕs Points - School store -- pencils 15 cents and erasers 25 cents; relatives

Using manipulatives - a balance scale approach. Solve: x+2=6, x-2=7, x+3=-8, x-4=-9, 2x+4=x+5, 3x+2x=x+8, 3x+-2x=-x+8, 2x+6=-x, 2x+3=2x-5, ...

Balance scales continued

Week 7

Virtual balance scales

Virtual balance scales

Issues with balance scales: can you move from one side to the other?

Issues with balance scales: negatives?

Week 8

Alge-blocks

Algeblocks - multiplying terms

Algeblocks - factoring

Week 9

Algeblocks - what is a cubic

Algeblocks - maybe a surprise quiz?

Three island problem Building Houses and I Spy Patterns (from NCTM Navigations through Algebra in grades 3-5)

Week 10

Three island problem Building With Toothpicks and Exploring Houses (from NCTM Navigations through Algebra in grades 6-8)

Beams

Beams

Week 11

Review algeblocks, islands, balance scales, patterns, ...

Squares Cubed (from NCTM Navigations through Algebra in grades 3-5)

Bouncing Tennis Balls and Triangle Rule Machine (from NCTM Navigations through Algebra in grades 3-5 & 6-8)

Week 12

Review Houses on Islands problems

Relating intuition and algebra

Wrap-up Triangle rule machine

Week 13

Wrap-up bouncing tennis balls -- regression on calculators

Line of best fit -- slope and intercept

Wrap-up slope and intercept