algebraic reasoning january 6, 2011. state of texas assessments of academic readiness (staar) more...

Algebraic ReasoningJanuary 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 schoolTwelve 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 StandardsReadiness 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 only2x + 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 AlgebraArticle: “Improving on expectations: preliminary

results from using network-supported function-based 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 Symbols3. Study of structure in the number system4. Study of patterns and functions5. Process of mathematical modeling,

integrating the first four list itemsKaput (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.