This document provides an overview of a teacher's training, philosophy on teaching algebra, units taught, and results from implementing a functions-based approach to teaching algebra. The teacher has taken several courses related to curriculum, instruction, and assessment. Their philosophy is to use a functions-based approach to help students make their own associations and build patterns, using visualization and context to give meaning to algebra. Units covered include families of functions, linear, absolute value, systems, exponential, quadratic, polynomial, and radical functions. Test results showed students scored higher using the functions-based approach, particularly co-taught students. The teacher reflects on personal and professional growth from implementing this approach.
2. History/Training
Algebra for All
Year 1
Year 2
Master’s Work
Curriculum, Instruction, and Assessment
MAT – Master of Arts in Teaching
Online PD last year
EMATHS – Implementing Algebra Units
Project PRIME
3. Philosophy
What is a Functions Based Approach?
Content
Instruction
Reasons for Using a Functions Based Approach
We remember Algebra longer when make and use our own associations
Pattern Building makes learning simpler, faster, understandable
Graphing Calculator and effects of engagement
Use of visualization first and symbolic second
Function implementation module and early activities prime the brain
for algebra that follows
Enriched learning environment
Contextual situations (represented as functions) help give
meaning to the algebra
Laughbaum, E.D. Why Use a Function Approach when Teaching Algebra. Texas Mathematics
Teacher, 53(1), 10 - 16
4. Units
1) Family of Functions
2) Linear Functions and Equations
3) Absolute Value Functions and Linear Inequalities
4) Systems of Linear Equations and Inequalities
5) Exponential Functions
6) Quadratic Functions and Quadratic Equations
7) Polynomial Functions
8) Radical Functions and Equations
9) Bi-variate Data and Mathematical Modeling
5. Unit 5 – Exponential Functions
Lesson Type of Lesson
Let’s Make a Deal with Your Parents Investigation
Pay It Forward Investigation
Bee Gone? Investigation
Transformations with Online Graphing Investigation/Notes
Calculator
Quiz: Exponential Growth and Assessment
Decay/Transformations of Exponential
Functions
HW: Which Family of Functions is it?
6. Unit 5 – Exponential Functions
Lesson Type of Lesson
Properties of Exponents Notes
Practice with Properties of Exponents Group Work
Properties of Exponents Notes/Group Work
Properties of Exponents Practice: Fraternal Twins Group Work
Quiz: Properties of Exponents Assessment
HW: Pre-Scientific Notation
Scientific Notation Notes/Investigation
Exponential Growth and Decay with Percentages
HW: Finish investigation
Percent Increase and Decrease Notes/Group Work
Review Group Work/Individual Practice
Unit 5 Test: Exponential Functions Assessment
7. Unit 5 – Exponential Functions
**Exponential Activity Assessment somewhere in unit? (did
not do but would like to)
Exponential Activities that we have:
Pay it Forward Video clip
One Grain of Rice Book
Alice and Wonderland Video Clip or Book
Make a Deal with your Teacher
Paper Folding Mythbusters Video Clip
M&M Hands on with M&Ms
Lily’s Mussels
USA Today- Population Uses Census Data
Bee Gone
9. Video Reflections
What are the different ways students are asked to
record information?
What are some methods used to keep all students
engaged?
What percentage of students involved in the board
activity in the co-taught class do you think are
students with special needs?
Can you see any examples that demonstrate students’
comfort level with math conversations?
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15. 1st Semester Results
PLC/Function Based
Algebra 1 PLC Functions Based
Students scores were higher Students scores were higher
by at least 5% on 9 out of 50 by at least 5% on 13 out of 50
questions questions
Co-taught students scores Co-taught students scores
were higher by at least 5% on were higher by at least 5% on
13 out of 50 questions 24 out of 50 questions
16. Comparisons
PLC Function Based
Solving absolute value Graphing linear functions.
equations. Horizontal and vertical lines.
Solving a linear equation with Writing an equation for a
a fraction. linear situation in real-life.
Proportion to solve Correlation of scatter plots.
contextual problem. Simplify an expression using
order of operations.
17. Things that were not explicitly
addressed but did comparably…
Unit rate
Ordering numbers from least to greatest
Perfect squares
Finding the length of a square mirror if the area is given
Giving coordinates of a point
18. Michigan Algebra 1 Assessment
Content 2010 – 2011 2011 – 2012 Change
Follow Pattern in Table 72 78 + 6%
Relationship in table 73 60 - 7%
Which family of function? 55 46 - 9%
Follow Pattern in Table- Linear 17 48 + 31%
Write Equation Perpendicular 50 48 - 2%
through a point
Graphing Linear Equations 50 71 + 21%
Which function is it? 82 95 + 13%
Horizontal/Vertical Linear and 58 76 + 18%
Parallel
Correlation Strength 50 80 + 30%
Graph Linear Equations 75 86 + 11%
Scatterplots-modeling 33 54 + 21%
Correlation – interpreting the 25 58 + 33%
situation
EMILY: Noah and Emily A4A. Year 1 – the content. Year 2 – how to implement it. Jess and Sarah’s Masters work. Then when we did our online PD together it also focused on algebra units. Realized we all were interested. Presented to Department- Noah wanted in. Then EMATHS this summer. Prime – how it leads into Geometry and Algebra II (?Should I include?)
NOAH: Turn to “family of functions” in note packet - Highlight Family of Functions Unit – interpreting graphs!!!! Identifying which functions is different… then shapes of each function graph… and symbolic.Talk about ending each unit with Linear or not? Linear Absolute Value or Not? Linear, absolute, value, exponential or not? Etc.
JESS
JESS
SARAH?!?!?! I think handouts here would be great. 1. Filling the swimming pool (tables help special ed students enter the problem) 2. System of Linear Inequalities Performance Task 3. Linear Test? -Refer back to Unit 5 outline and how much notes/investigations/etc.-Notes Handwritten v Guided-Homework – Assign less in beginning and them more later once have mastered!! spiraling -Investigations – Engagement??-Assessments – Putting things on but not “grading” because not expecting mastery…. Putting things on that they have never seen before but have skills to complete (how similar to common core – only can perservere if have never seen problem again)
EMILY: Noah and Emily A4A. Year 1 – the content. Year 2 – how to implement it. Jess and Sarah’s Masters work. Then when we did our online PD together it also focused on algebra units. Realized we all were interested. Presented to Department- Noah wanted in. Then EMATHS this summer. Prime – how it leads into Geometry and Algebra II (?Should I include?)
NOAH: Mainly mention how we did as well as PLC. Mention Mike Bender’s concern when we started this was that the Special Education students would be confused with the context and words. We answered him with we don’t know… but research says they should do better. And now……
JESS
JESS: Talk about none of these are one lessons…. Save time as INCORPORATING throughout (x and y intercepts)
SARAH: Emphasize we gave this at the semester… we will give again at the end of the year… how some results will be different. Our “pluses” might not be as great of pluses….. But how the minuses we haven’t taught yet. SARAH- talk about perpendicular with tables
EMILY: See attached notes
I’m thinking each of you could talk for 30 to 60 seconds regarding one of these topics or something similar.Personal Growth (). Professional Growth (Jessica). Challenges (Emily). Beliefs… about student learning… math knowledge…. Teacher isn’t end all be all (Social Ed kids can do so much; we can’t write them off).