are you ready for the new mathematics requirements? 2008 superintendent's summer institute...
TRANSCRIPT
Are you ready for the new mathematics requirements?
2008 Superintendent's Summer Institute August 5, 2008 Oregon Convention Center
Teachers Inspiring Problem SolversCathy Brown, President
What are the new graduation requirements for mathematics and when do they start?
Students who are in grade 11 during the 2008-2009 school year must:
Have 3 years of mathematics to graduate.
What are the new graduation requirements for mathematics and when do they start?
Students who are in grade 9 during the 2008-2009 school year must:
Have 3 years of mathematics – addressing the revised mathematics standards
-- to graduate.and Demonstrate Proficiency in the Essential Skill – Apply mathematics in a variety of settings #
What are the new graduation requirements for mathematics and when do they start?
Students who are in grade 7 during the 2008-2009 school year must:
Have 3 years of mathematics – at the Algebra 1 content level and above*
-- to graduate.and Demonstrate Proficiency in the Essential Skill – Apply mathematics in a variety of settings #
What’s the definition of “Apply mathematics in a variety of settings”?
• Interpret a situation and apply workable strategies using appropriate technologies
• Produce evidence – graphs, models, to obtain and verify a solution
• Communicate and defend the verified process and solution using pictures, symbols, models, narrative or other methods
#--demonstrate mastery of the Essential Skill: Apply mathematics in a variety of settings:
Completing an approved, locally scored assessment, such as a work sample [scored using the official state scoring guide] or student project
-- or --
Achieving a state-determined score on the OAKS state assessment in mathematics
-- or --
Achieving a state-determined score on other standardized tests (SAT, IB, AP + more options)
Work Samples?Math Problem Solving work samples (scored w/official state scoring guide)
remain a requirement: 1 each at grades 3 – 8
and 2 in high school
*The 3 years of mathematics – at the Algebra 1 content level and
above:Has been defined as:
– Algebra 1, Geometry, Algebra 2Or– Electronics, Construction Mathematics, etc – IF
they meet the same academic standards as above
Thinking about your district:
• About what fraction (percent) of students currently, successfully complete 3 years of high school math?
• About what fraction (percent) of students currently, meet standard on OAKS and/or meet standard on 2 MPS work samples?
• About what fraction (percent) of students currently, successfully complete 3 years of math at the Algebra 1 level and higher?
Thinking about: students successfully completing 3 years of high school math?
• Are the 3 years of mathematics offered in your district, the “best” for all students to be successful in whatever their next steps?
• Why Algebra 2?• Are there other options?
One option: Mathematics 1, 2, 3
• Algebraic Structures & Number Systems• Functions and Analysis• Geometry & Geometric Measurement• Data, Statistics, and Probability
Another: Algebra 1, Geometry, Algebra 2
NCTM Policy Statement
Excellence in mathematics education rests on equity—high expectations, respect, understanding, and strong support for all students.
Policies, practices, attitudes, and beliefs related to mathematics teaching and learning must be assessed continually to ensure that all students have equal access to the resources with the greatest potential to promote learning.
Questions to be answered:• Are the current mathematics course options
serving all students?• Who needs to be in the conversations about
any change?• What steps are needed to keep the parents
both informed and supportive?• How will the teachers be supported?• How will the students be supported?• Who teaches which students?
What are some options for the students that “might not get there”?
First, let’s see what the research says . . .
Catching Up
• Students with a history of going slower are not going to catch up without spending more time and getting more attention.
Situation of S Needed by S Intervention for S
Keeps up Regular Instruction None
Struggles some assignments
Extra feedback on work, thinking
Classroom Q&A, partner, teacher’s ear
Not bringing enough from earlier lessons each day
Extra support with regular program before, during, after class
Homework clinic, tutoring, attention beyond regular class
Misconceptions from earlier grades disrupt participation
In-depth concentration on troublesome concepts
Sustained instruction with special materials beyond regular class
More than a year behind, too many misconceptions from earlier grades
Intensive course Double period ramp-up course, Extended day,
Summer schools
Intensification
Why do students struggle?
• Misconceptions• Bugs in procedural knowledge• Mathematics language learning• Lack of knowledge (gaps)• Disposition, belief, and motivation
Again, let’s see what the research says . . .
Misconceptions:
where they come from and how to “fix” them
Misconceptions about misconceptions
• They weren’t listening when they were told/taught
• They have been getting these kinds of problems wrong from day 1
• They have forgotten• The “other side” in the math wars did
this to the students on purpose
More misconceptions about the cause of misconceptions
• In the old days, students didn’t make these mistakes
• They were taught procedures• They were taught rich problems• There was not enough practice
In addition:• There’s not enough time in the day• “Everyone can learn” – do we really
believe that?• “Mile wide & inch-deep” curriculum
causes haste and waste• Inequality in materials/manipulatives• Professional development needs to be
ongoing
Whatever the Cause• When students reach class they are not
blank slates• They are full of knowledge• Their knowledge will be flawed and
faulty, half baked and immature; but to them it is knowledge
• This prior knowledge is an asset and an interference to new learning
Content: Foundations• Use simple algebraic reasoning to repair and
strengthen students’ arithmetic foundations:– Extensive use number line to revisit number
concepts and transfer to knowledge of coordinate graphs
– Explicit use of number properties and properties of equality in reasoning about arithmetic and transfer to reasoning with letters and expressions that represent numbers in algebra
– Use good problems to teach path from concrete reasoning to symbolic expressions of algebra
For example
Suppose you know that Lisa is 63 inches tall. With shoes on, Lisa will be taller; but how much taller? That depends on how tall her shoes are.
Lisa’s height = 63 inches + shoe heighth = 63 + s
Misconception Learning verses Remedial Learning: Test Scores
10.4
17.819.1
7.9
15.8
12.7
0
5
10
15
20
25
Pre-test Post-test Delayed Test
Students who weretaught by addressingmisconceptions
Students who weretaught using remedialmeasures
Research on Retention of Learning: Shell Centre: Swan et al
Wrong Answers
• Are part of the process, too• What was the student thinking?• Was it an error of haste or a
stubborn misconception?
What is conceptual consistency?
Curriculum is a ‘mile deep’ instead of a ‘mile wide’–Apply one profoundly important concept in
100 situations rather than memorizing 100 procedures that do not transfer– Typical is to opt for short-term efficiencies–Result is students don’t remember what
they ‘learned’ later
Interpreting Multiple Representations
Key features of a well designed intervention
• Lean and clean lessons that are simple and focused on the math to be learned
• Rituals and Routines that maximize student interaction with the mathematics
• Emphasis on students, student work, and student discourse
What NCTM says about Intervention
NCTM firmly believes that all children can learn.At the same time, the Council understands that not all students learn at the same rate or in the same way. In the gradual journey toward mathematical understanding, students may experience difficulties that require intervention. Moreover, some talented students may need opportunities to be accelerated beyond the curriculum that other students follow.
An Intervention Program
An intervention program can be thought of as a cycle consisting of three phases: –Diagnostic assessment –Instructional actions and
alternative approaches –Follow-up assessment
Motivation
• Respect the students & recognize their frustrations with mathematics
• Easy problems on advanced topics
• Engage students in the mathematics
For example:Subtracting a negative number is the same as adding a positive number.
3 – (-2) is the same as 3 + 2On a number line, find -2 and find 3, the distance between them (the difference) is 5.
On a number line, find 0 (the starting place), move to 3 and then move 2 more. Again the difference (between 0 and 5) is 5.
So . . . • Where are your students?• What timeline will you use to provide all
students the opportunities they need to be able to graduate?– What will you do first?– Who will help?– What “materials” will you use?– How will you communicate what the changes are?– What professional development is needed?
Some potential resources• NCTM Addenda Series “A Core Curriculum”• America’s Choice – Ramp-Up series• Math Learning Center – Visual Algebra• NCTM Navigation Series• http://www.utdanacenter.org/k12mathbenchmarks
• Washington – “if grade 8 is Algebra” then, this is the impact on grades 6 & 7
• Others?
Thanks!