Transcript Algebraic Reasoning - Seguin Independent School District

Algebraic Reasoning
January 6, 2011
State of Texas Assessments of
Academic Readiness (STAAR)
• More rigorous than TAKS; greater emphasis on
alignment to college and career readiness
• Grades 3−8
Tests are in same grades and subjects as TAKS
• High school
Twelve end-of-course assessments in the four
foundation content areas—mathematics, science,
social studies, and English—replace the current high
school TAKS tests
NEW ASSESSMENT DESIGN—STAAR
• “Fewer, deeper, clearer ” focus
• Linked to college and career readiness
• Will emphasize “readiness” standards, defined as
those TEKS considered critical for success in the
current grade or subject and important for
preparedness in the grade or subject that follows
• Will include other TEKS that are considered
supporting standards and will be assessed, though
not emphasized
Readiness & Supporting Standards
Readiness standards have the following characteristics:
• They are essential for success in the current grade or course.
• They are important for preparedness for the next grade or
course.
• They support college and career readiness.
• They necessitate in-depth instruction.
• They address broad and deep ideas.
Supporting standards have the following characteristics:
• Although introduced in the current grade or course, they may be
emphasized in a subsequent year.
• They play a role in preparing students for the next grade or
course but not a central role.
• They address more narrowly defined ideas.
STAAR
Digging Deeper
• Study the documents both vertically
and horizontally. What conclusions
can you draw?
• What implications does this have for
our work?
• Share your thinking.
STAAR: Griddable Items
High School: 5 Griddable Items
Math Categories
TAKS Blueprint vs. STAAR
Algebra Readiness Components
• Texas Response to Curriculum Focal Points
(TxRCFP)
• Math Professional Development Academies
• MSTAR Universal Screener
• Project Share (MSTAR academies, OnTRACK
courses, etc)
• RTI
TEKS PD Workshops in 2011
Algebraic Reasoning: A
Function-Based Approach
Why Use a Function Approach when
Teaching Algebra?
• Read 1-page overview
independently
• Share your thoughts with a partner.
• Why should we use a function
approach when teaching Algebra?
Engage Activity
• Simplify the expression x + x + 3 using paper
and pencil only
2x + 3
• How do you know if you’re correct?
• How can students check to make sure they
have simplified an expression accurately?
• Input each expression into Y1 and Y2.
• Graph them and examine their tables
• What do you notice?
Engage Activity Cont.
If the expression x + x + 3 is equivalent to the
expression 2x + 3, then the function f(x) = x + x + 3
and the (simplified) function g(x) = 2x + 3 have
graphs that are exactly the same.
** Any thoughts?
Research on Function-Based Algebra
Article: “Improving on expectations: preliminary
results from using network-supported functionbased Algebra”
• ALL
– Read 1.0 Introduction (p. 1)
• Partner 1
– Read 2.0 Background starting at Function-Based
Algebra Revisited (pp. 2-3)
• Partner 2
– Read 2.0 Background starting at Supporting
Generative Design with TI-Navigator (pp. 4-5)
Moving towards a Function-Based
Approach
• Algebra Strand in Elementary Mathematics
(NCTM, PreK-12)
• Rich algebra experiences in the early grades
• Integrating technology to enrich algebraic
thinking
• Integrating Algebra experiences in other
content areas and other math strands
• Focus on mathematical modeling
Algebraic Reasoning
1. Generalization from arithmetic and from
patterns in all mathematics
2. Meaningful use of Symbols
3. Study of structure in the number system
4. Study of patterns and functions
5. Process of mathematical modeling,
integrating the first four list items
Kaput (1999)
Technology
Technology is an essential tool for learning
mathematics in the 21st century, and all schools
must ensure that all their students have access to
technology. Effective teachers maximize the
potential of technology to develop students’
understanding, stimulate their interest, and increase
their proficiency in mathematics. When technology
is used strategically, it can provide access to
mathematics for all students. NCTM Position Statement on the Role
of Technology in the Teaching and
Learning of Mathematics (March 2008)
Tools for Enriching Algebra Experience
• Graphing calculators, CBRs, etc
• TI Navigator
• Computer Applications and Software
(Geometer’s Sketchpad, Cabri Geometry, etc)
• Web (National Library of Virtual
Manipulatives, NCTM Illuminations, data
graphers, applets, etc)
• Podcasts
Resources
• TIMath.com
• Activities Exchange
(education.ti.com/exchange)
• TIMiddlegrades.com (TI-73 Activities)
• Student Zone (education.ti.com/studentzone)
• TI 84 New OS 2.53
• T^3 Online Course (Using TINav System)
Polynomials
Discussion Points
• Why is it critical to begin exploration of an
algebra concept with concrete manipulatives,
then move towards the pictorial and finally
the abstract?
• How is mathematical modeling involved?
• Why is it important for students to make
connections between various representations
of algebra concepts?
Quadratic Functions
Discussion Points
• What patterns did you notice in the models
you constructed?
• How did the patterns in the models relate to
the patterns in the table and function rules?
• How do the rules, graphs, & rates of change
compare for perimeter and area?
Discussion Points
Reflections
• What are some of the implications of the new
STAAR assessment program?
• How can we dig deeper when teaching algebra
so that our students have a better
understanding?
• What are some strategies we can use to help
students conceptually understand algebraic
structures?
Next Meeting
• Bring a sample of student work related to the
concepts we discussed today.
• Be prepared to share at least 1 thing you have
implemented in your teaching from this
training.