WEBVTT

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[Music] Welcome to the overview

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on Multiple Pathways to School Algebra.

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District math supervisor Kim Brackett

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recently asked mathematics teachers

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to identify where the topics

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of school algebra were discussed

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in the curriculum.

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What she got was a whole new perspective

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on how algebra is being taught

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in her district's middle

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and high schools.

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She learned from her teachers

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that the algebra sequence

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in some high schools was much more

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rigorous than in others.

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In some cases,

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there were articulation problems,

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so that students moving from Algebra I

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in one middle school might be required

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to repeat the same topics

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when they reached high school.

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She also found that some

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of the algebra topics recommended

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by the National Mathematics Panel were

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not being addressed

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in the district's math courses.

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Ms. Brackett believes proficiency

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in algebra is the best way

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to secure future education

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and career options for all students.

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This is why working

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on the district-wide progression

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of school algebra topics is now her

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number one priority--

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a task that requires attention

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to content coverage, text materials,

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alignment of instruction

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and assessments,

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and professional development.

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These changes will require a unified

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perspective on the part of district

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and school leaders.

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They will need to share a common belief

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about the position of algebra

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in the education of all students.

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To find out more and get support,

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Ms. Brackett consults

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with the state supervisor

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of mathematics,

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who shares the major tenets

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and implications

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of the National Mathematics Panel

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report, especially those having to do

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with state mathematics standards.

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The National Mathematics Advisory Panel

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provides expert judgment

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about the content of school algebra,

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suggests implementation considerations

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for practitioners, and reviews research

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about the learning of algebra.

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The Report speaks to high expectations

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for students, clarifies course

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configuration options,

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emphasizes the importance

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of pre-algebra preparation,

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and provides information teachers need

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about diagnosing common student errors.

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One of the fundamental elements

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of successful algebra instruction is

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high expectations.

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Teachers must believe

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that all students can be successful

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in learning algebra.

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All secondary students must be given the

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opportunity to master all the topics

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typically included in Algebra I

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and Algebra II.

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This does not mean

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that all math programs need

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to be identical.

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The Panel notes

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that different configurations

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of mathematics courses can be

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employed effectively.

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School algebra is traditionally

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organized into two single-subject

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courses, Algebra I and Algebra II.

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In other schools,

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the content of school algebra is

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interwoven with geometry, statistics,

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and other mathematical topics

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in integrated mathematics courses.

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There is no basis in research

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for one particular configuration

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of topics over another.

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The important point is

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that all recommended topics

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of school algebra are addressed.

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It is vital that the structure

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and implementation

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of algebra course offerings should allow

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for differentiated instruction.

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Teachers cannot assume that all students

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in a grade level have the same degree

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of preparation in the principles

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of arithmetic that are critical

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for learning algebra.

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They must be able to respond flexibly

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to the different levels and abilities.

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Those students who are not ready

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for algebra will require additional

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instruction and more practice

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to develop critical foundations

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of algebra, including number sense

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and proficiency with fractions.

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Students who are mathematically gifted

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and who readily grasp algebra concepts

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should have the opportunity to work

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at an accelerated pace,

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mastering school algebra topics

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at a faster rate and moving

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on to study advanced topics

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of mathematics.

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Students who are enrolled

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in an algebra course

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and struggling need options for support,

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including opportunities

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for intensive instruction

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in the principles of arithmetic

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that are fundamental

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to grasping algebra concepts.

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Support can take many forms:

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refreshers of arithmetic concepts

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learned previously,

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practice with algebra terms,

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and connections to prior learning;

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Intense preparatory experiences

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in the form of summer

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"algebra boot camps" or algebra labs;

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and Daily remediation periods.

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Of course, in order to be this flexible,

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teachers need to be able

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to recognize students' misconceptions

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and errors in algebra problem solving

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and diagnose

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underlying misunderstandings.

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The report describes some common errors

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in algebra problem solving

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that are based on underlying confusions

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with arithmetic principles

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and procedures.

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Many students, for example,

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have not developed understanding

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of the syntax of algebraic expressions,

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including confusion about the concept

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of mathematical equality and whether

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to interpret the equal sign

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as an expression of relationships

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or a call to take particular actions.

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Further, students frequently make

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mistakes when dividing terms

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that include a coefficient

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and a variable

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and have difficulty determining the

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appropriate application

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of the commutative

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and distributive properties.

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Problems can occur

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when students over-generalize the use

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of particular procedures

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or have a misunderstanding

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of a procedure,

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such as those for

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transforming equations.

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These mistakes are sometimes referred

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to as "procedural bugs"

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or misconceptions.

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Teachers need to understand how students

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learn to solve equations

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and word problems and need to know how

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to recognize common sources of errors

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and conceptual misunderstandings.

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Teachers with this type

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of training are better able

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to anticipate the types

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of errors students may make.

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Instruction that focuses

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on particular procedural misconceptions

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has been shown to reduce the frequency

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of student errors.

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In conclusion:

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The National Mathematics Panel report

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provides more than a list

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of recommended school algebra topics.

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It clarifies course configuration

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options, emphasizes the importance

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of pre-algebra preparation,

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and provides information

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about common student errors

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and the clues they offer

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about remediation and preparation.

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Ms. Brackett's conversation

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with the state supervisor

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and her own study

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of the math panel report gave her

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insight that will guide her work

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on revamping the district's approach

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to algebra instruction.

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She is much more secure

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in allowing district schools

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to continue the course configurations

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they have in place as long as they focus

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on all recommended topics

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of school algebra.

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She will work with school mathematics

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leaders to review the adequacy

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of preparation for algebra,

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the current options for acceleration

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for mathematically gifted students, and,

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most urgently,

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how struggling students can receive

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immediate attention.

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To learn more about Multiple Pathways

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to School Algebra please explore

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the additional resources on the

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Doing What Works website.