WEBVTT

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[Music] Welcome to the overview
on school algebra topics.

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"The state board of education 
wants to make modifications

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in algebra content standards
and assessments so they will line

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up better with the National Mathematics
Panel's recommendations.

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"We need to make sure we're ready
for this change."

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With those words, district 
math supervisor Kim Brackett

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opened a day-long in-service 
for middle and high school

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mathematics
department staff.

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Ms. Brackett reviewed the school algebra

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topics that have been recommended
by the Panel.

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She then challenged school teams to 
figure out how well the district was

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doing in terms of topic coverage
and where they needed to improve.

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Using the topics associated
with quadratic equations,

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Ms. Brackett demonstrated how school
teams should structure their reviews.

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She showed them a table
with topics recommended

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by the Math Panel listed
in the first column

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and in the second column,
whether or not that topic

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is covered in the current 
state standards.

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In the last three columns,
teams are instructed to identify

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in which math courses the various 
topics are addressed.

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Ms. Brackett reminded teams
that a topic is "addressed"

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in a course only if students are 
expected to become proficient

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in the skills associated 
with the topic.

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The teams were given time to confer
and consult their objectives,

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pacing charts, and textbooks.

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After getting a show of hands,
Ms. Brackett completed the table,

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mapping how each school was 
addressing quadratic equations.

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They found that two of the 
topics are not currently

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addressed in state standards
and that there was a lot of variation

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within the district
in terms of coverage.

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One topic in particular was not well
addressed in district courses.

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Ms. Bracket repeated this process
with her team, reviewing each

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of the other school mathematics topics
recommended by the National Math Panel.

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Let's take a look at the specific topics 
identified by the Math Panel Report.

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To develop the list
of recommended school algebra topics,

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the National Math Panel reviewed state
standards, the National Assessment

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of Educational Progress algebra
objectives, the American Diploma Project

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benchmarks, and the Singapore
mathematics curriculum.

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The panel of mathematicians
and mathematics educators applied

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their combined professional 
judgment to those findings

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to determine a final set
of recommended topics.

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The National Math Panel identified 
six primary topic headings.

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The headings are:
Symbols and Expressions,

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Linear Equations, Quadratic Equations,
Functions, Algebra of Polynomials,

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and Combinatorics and Finite 
Probability. Each of these headings

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is further broken down into 
series of topics.

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For Symbols and Expressions,
there are three important topics,

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including polynomial and rational 
expressions,

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and arithmetic and finite 
geometric series.

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The heading of Linear Equations
encompasses a number of topics dealing

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with solving and graphing linear 
equations as well as linear inequalities.

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The heading of Functions covers 
a number of topics such as linear,

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quadratic, and many other 
nonlinear functions.

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It also includes fitting simple
mathematical models to data.

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Algebra of Polynomials and the 
joint heading of combinatorics

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and Finite Probability are the 
last two headings identified

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by the National Math Panel,

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each containing their own lists
of sub-topics.

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The research done by the National 
Math Panel turned up

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more than a list of important 
headings and topics.

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The panel report emphasizes the
importance of making

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connections among the topics.

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For example, the method of solution
for Linear Equations is applicable

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to Quadratic Equations and leads
to the well-known quadratic formula.

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Also, completing the square connects
topics in Quadratic Equations

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with topics under Functions 
and Algebra of Polynomials.

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National Math Panel task group 
members reviewed research

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about how students learn algebra.

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Out of this review, the report 
offers insights for teachers

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about building students' proficiency
with the topics of school algebra.

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A consistent theme emerging
from this research is the importance

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of particular types of practice.

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Developing proficiency in algebra 
depends on cumulative practice.

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Students who are skilled
in problem solving have developed

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long-term memory of basic 
forms of equations and

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the procedural steps
used to solve them.

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Many students however will 
need extensive practice

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to develop this ability
to automatically recognize the forms

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of equations and word problems 
and how to approach them.

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For students who need practice
in basic transformations

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of algebraic expressions, worked-
out examples with explanations

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and procedural steps can be a
powerful aid.

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For example: in a homework assignment,
a teacher might provide a few fully

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worked-out, step-by-step solutions
for algebraic problems along

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with several similar problems
for students to solve on their own.

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Proficiency in solving word problems
requires a specific type of practice:

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the accurate translation of problems.

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In other words, students need 
practice identifying what

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information is relevant
in a word problem

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and then developing the 
corresponding symbolic notation.

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While students need practice 
translating all the various

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types of statements in problems, 
research has found that they tend

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to have particular difficulty
with translating relational statements.

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Consider this example
of a relational statement.

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Using f for the number of feet
and y for the number of yards,

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write an equation for the 
relationship between these units.

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What can we take away from this?

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In any district's mathematics
 program, it is important

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to identify the critical topics
of instruction,

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how they support each other,
and how to help students focus

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practice to master the topics.

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The National Math Panel Report 
provides information about

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the key topics of school algebra 
along with other suggestions

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for implementation.

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While Ms. Brackett was pleased
with teacher response

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to the in-service day, it was 
clear that there was much work

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to do on the district's algebra
curriculum due to changes

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in state standards.

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She could see that in some schools,
there was need for more work

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on articulation across algebra 
topics and courses.

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She decided that she'd need
to contact the state mathematics

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supervisor with the results
of the district review and

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seek advice about next steps.

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To learn more about school algebra
topics please explore the additional

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resources on the Doing What
Works website.