Sep 7, 2017 - Identify examples of deficit language and develop strategies to remove it .... decimals independently in 3
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