De-tracking Elementary Mathematics

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De-tracking Elementary. Mathematics. September 7, 2017. Mark Alcorn. Mathematics Coordinator. San Diego County Office of
De-tracking Elementary Mathematics September 7, 2017 Mark Alcorn Mathematics Coordinator San Diego County Office of Education [email protected] @mark4math #detrackelementarymath

High Expectations

Outcomes LANGUAGE MATTERS • Identify examples of deficit language and develop strategies to remove it from your environment GROUP FOR SUCCESS • Learn how some math grouping structures can reinforce low expectations, and understand ways to make grouping more effective for ALL students TASKS DICTATE EXPECTATIONS • Learn how high-quality tasks provide better support for ALL students

Language Matters “I need to share some things with you about the low math students you will be getting next year…”

What is the phrase “high math student” even mean?

How are we defining success in mathematics ? • Success in timed multiplication fact tests? • Success in getting answers the first time without errors? • Success in justifying an answer? • Applying mathematics to the real world? • Getting the right answer quickly 9/10 times? • Successfully searching and finding patterns?

What do mathematicians do? • Take risks • Make mistakes • Are precise • Rise to a challenge • Ask questions • Connect ideas • Use Intuition • Reason • Prove • Work together and alone

Changing the future

New York Times – 8/24/17

Impact your environment • Pair up and role play how you will respond to a situation in your

job environment in which “language matters”

• Be prepared to share the best practices you develop in your

team with the rest of us

Group for Success

“85% of United States Schools separate students based on presumed ability.” – Principles to Actions: Ensuring Mathematical Success for All (NCTM)

Cooperative or Collaborative Partnerships? • Does the math task demand a collaborative team effort? • Is the implied or explicit expectation for one student to tutor

the other student within the partnership?

• How is each student being held accountable for their

collaboration?

• Do students recognize the benefit of the collaborative team

effort in engaging in the math task?

“It is hard to have a growth mind-set when you are in the low math group.” – Dr. Julia Aguirre

Just-in-time intervention • Using formative assessment drives meaningful small groups • Small groups allow students to practice and receive feedback

regarding collaborative work

• Allowing students to opt-in to small groups reinforces flexible

groupings and rewards students who track their own learning

• Peace-sign collaborative groups is an effective structure while

managing small groups

Reflection • What does this discussion affirm about your

thinking and implementation of grouping structures?

• How does this discussion challenge your

rationale regarding grouping and how to implement grouping structures?

Tasks dictate expectations

Rock & Roll Marathon

My friend, Kevin, is doing training runs to prepare for the Rock and Roll Marathon on Sunday, June 5. He is trying to figure out whether he will run out of water during his training sessions. Develop some questions you would ask him to help him to figure this out:

Rock & Roll Marathon Kevin drinks two thirds of a cup of water for every mile he runs. His water bottle holds 4 cups of water. How many miles can he run before he runs out of water?

Draw a picture or model first to represent the situation:

Characteristics of a High-Quality Task What language would you use to describe the characteristics of the task, “Rock and Roll Run”?

Multiplication/Division Concepts 1st

Fraction Concepts

2+2+2=6

2nd

one half is shaded 2+2+2=6 two-thirds is shaded

3rd

3 x 2 = 3 groups of 2 = 6 2 x 3 = 2 groups of 3 = 6 2/3 is shaded

6 ÷ 2 = How many groups of 2 in 6 OR 6 ÷ 2 = If I divide 6 equally into 2 groups, how many in each group? 3 x 2/3 = 3 groups of 2/3 = 2

4th

5th

How many groups of 2/3 are in 4?

... 1 group

2 groups

3 groups

Some characteristics of a high-quality mathematics task • Reflects high cognitive demand (Stein et. al., 1996) • Allows multiple ways to enter the task and to show competence (Lotan, 2003) • Provides access to a wide range of learners (Piggott, 2012) • Encourages creativity and imaginative application of knowledge (Piggott, 2012) • Exposes what students know and provides information for next steps (Hiebert, et. al., 1997) • Encourages reflection and communication (Hiebert, et. al., 1997) • Promotes connections between two or more representations (Lesh, Post & Behr, 1988) • Leaves behind something of mathematical value (Hiebert, et. al., 1997)

High-quality tasks allow for access and extension

How do IEP goals dictate expectations? Sample of a current 5th grade goal:

By June 2017, ________ will add, subtract, multiply and divide multi-digit whole numbers with regrouping and decimals independently in 3 out of 5 trials with 75% accuracy as measured by teacher-made assessments and/or student work samples.

How do current IEP goals limit student expectations? • Many IEP goals are written based on a procedural skill devoid

of understanding

• This narrow skill can determine a year-long focus for the

student at the exclusion of other mathematics learning

• Prolonged focus on one narrow skill can limit a student’s view

of mathematics and their potential to be successful

th Revised 5 grade IEP Goal

Sample of a revised 5th grade goal: By June 2018, _______ will create a model/picture based on a story problem and use the model/picture to decide what operation to use to solve the problem 75% of the time when given 4 problems over one week as measured by student work samples.

Preparing ALL students • Which IEP mathematics goals will ensure that the student will

have access to the thinking and reasoning needed to be a successful mathematics student over the next 3 years?

• Which IEP mathematics goals will ensure that the student will

become a productive citizen?

Which area will you impact tomorrow? LANGUAGE MATTERS

GROUP FOR SUCCESS

TASKS DICTATE EXPECTATIONS

Let’s continue the conversation! In person:

Email: [email protected] Twitter: @mark4math #detrackelementarymath