LEARNING BY DOING MATHEMATICS - Carnegie Learning

Carnegie Learning ®
Blended Math Solutions
LEARNING
BY DOING
MATHEMATICS

The Need for 21 st Century Classrooms
Today’s students have grown up in a digital world where instant messaging and listening
to MP3s while doing homework is part of their studying routine. Students dislike
traditional classroom instruction where lectures are the primary mode for delivering
instruction. Instead, they prefer to have opportunities to work cooperatively and to learn
using technology.
Carnegie Learning ® Blended Math Curricula
We offer a unique solution to address the needs of today’s secondary students.
Carnegie Learning Blended Math Curricula provide a model for core math instruction
that is comprised of Carnegie Learning ® Textbooks and Cognitive Tutor ® Software. Our
standard implementation involves three days of collaborative learning in the classroom
and two days learning with our technology. Carnegie Learning offers blended solutions
for the following core math programs:
>> Algebra readiness (titled Bridge to Algebra)
>> Algebra I
>> Geometry
>> Algebra II
>> Integrated Mathematics I–III
Our unique approach for blending collaborative classroom instruction with
adaptive learning technology has been proven effective. The U.S.
Department of E ducation recognizes Carnegie Learning Algebra I as one
of the only math curricula that is scientifically proven to have significant,
positive effects on student learning. In fact, research has shown that
students using the blended Carnegie Learning ® Algebra I curriculum:
>> Demonstrate 85% better performance on assessments of complex
mathematical problem solving and thinking
>> Achieve 15-25% better scores on the SAT and Iowa Algebra Aptitude Test
The standard
implementation for
all Carnegie
Learning blended
curricula is three days
in the classroom using
the textbooks and two
days using the Cognitive
Tutor ® software.
>> Have a 70% greater likelihood of completing subsequent Geometry and
Algebra II courses
>> Perform 30% better on questions in the TIMSS assessment
In 28 years of teaching, I would have to
say that I’ve seen more students be
successful, I’ve seen more students know
mathematics than I ever have before.
And I think it wouldn’t be possible
without the integrated curriculum and
without the materials provided by both
the state and Carnegie Learning that we
are using.
Mark Argo
Math Teacher
Morgan County High School

Applied Research Model
& Evidence of Effectiveness
Carnegie Learning is the leader in using
cognitive science to develop a researchbased
model for how students learn.
This model is the foundation for
developing our adaptive technologies in
the Cognitive Tutor software. In fact, we
are the only publisher that has a
continuous improvement model for
enhancing our instructional software.
Annually, we’ve collected over 42
million observations of students’
studying (that’s approximately one
action for each student every seven
seconds). We use the data to enhance
our materials to provide the best fit for
how students learn.
In numerous studies, Carnegie Learning
solutions consistently have shown a
significant effect on student learning
outcomes resulting in improved
academic achievement in mathematics.
Please visit our research section of our
website at www.carnegielearning.com
to view or download the results.
Key Textbook Benefits:
>> Students like working cooperatively and become active participants in math class.
>> Students better relate to math when solving real-world problems.
>> Students make connections and understand key math concepts when they encounter
multiple representations.
>> Teachers are better supported with materials and tips for facilitating a collaborative learning
environment.
>> Consumable model allows for new textbooks annually – with meaningful updates made
each year.
Key Software Benefits:
>> Students must show mastery of each discrete skill required to solve math problems prior to
progressing through the software.
>> Delivers a mastery learning model within rich, rewarding problem solving contexts.
>> Uses true artificial intelligence to monitor student interactions and assesses skills to
individualize instruction.
>> Offers continuous, formative assessment throughout curriculum. Also includes summative
assessments.
>> Review Mode offers students the option to review and practice skills prior to exams.
>> Students can view their progress via the Skillometer which motivates them to do their best
work and master skills.
>> Teachers can review student performance data.
>> Teachers can modify assessments.
Key Professional Development Benefits:
>> Develop effective strategies for implementation of curricula.
>> Discuss student-centered classroom strategies.
>> Develop effective scaffolding and extension questioning strategies.
>> Integrate technology effectively into the instructional process to enhance understanding.
>> Improve teacher capacity including both content and pedagogical knowledge.

STUDENT
TEXTBOOK SET
Each student receives a textbook set
that contains the following three books.
Student Text
The Student Text is a consumable
textbook designed for students to take
notes and work problems directly in
each lesson. Each lesson contains
objectives, key terms, and problems that
help the students to discover and
master mathematical concepts.
Student Assignments
The Student Assignments book contains
one assignment per lesson and skills
practice activities. It is designed to move
with the student from classroom to
home to lab time so that students can
repeatedly practice the skills taught
in the lesson.
Homework Helper
The Homework Helper book is designed
to help parents and care givers be more
informed about the concepts being
covered in the student’s math course.
Students are encouraged to keep the
Homework Helper at home. It contains
one activity per lesson including
examples of the skills taught in the
lesson and several practice problems.
Answers to the practice problems are
provided in the back of the Homework
Helper book.
What Makes Carnegie Learning Student Texts Engaging
Learning By Doing ® Principals
Carnegie Learning believes that students develop math
understanding and skills by taking an active role and
responsibility for their own learning. With Carnegie Learning
textbooks students become engaged in solving contextual
math problems that strengthen their conceptual
understanding of math topics. Rather than encouraging
students to memorize procedures, we provide them
opportunities to think and work together in small groups.
Mathematical Discourse
Throughout the student text icons prompt different forms of
student communication. These icons may instruct students to
work independently, work with groups, or share ideas with the
class. Encouraging mathematical discourse provides
opportunities for students to explain their thoughts and
processes for solving math problems.
Real-World Context
Students work with their peers to solve real-world problem
situations like using percents for leaving a tip in a restaurant
or using a graph of an equation to determine the number of
days it will take to build miles of highway. They become more
engaged in learning mathematics when they see how it plays
a significant role in everyday life.
Think for
Yourself
Work With
a Group
Share With
the Class

TEACHER
TEXTBOOK SET
Each teacher receives a textbook set that
contains the following books.
Teacher’s Implementation Guide
The Teacher’s Implementation Guide
contains a lesson map for each student
text lesson. The lesson map includes
each lesson’s objectives, key terms,
NCTM standards, essential questions,
warm up questions, open-ended
questions, and closing activities. An
image of each student text page,
including answers, is provided in the
Teacher’s Implementation Guide.
Teacher’s Resources and
Assessments
The Teacher’s Resources and
Assessments book contains five tests per
chapter of the student text. The tests are
a Pre-test, a Post-test, a Mid-Chapter
Test, an End-of-Chapter test, and a
Standardized Test Practice.
The Teacher’s Resources and
Assessments book contains the
assessments with answers in place and
also includes answers in both the
student assignments and student skills
practice pages.
What Makes Carnegie Learning Teacher Materials Valuable
Student-Centered Classroom
In a student-centered classroom, the teacher facilitates
learning and coaches students to master math concepts and
procedures. Little time is spent on delivering lectures. Instead,
teachers lead students in completing task-based lessons and
fostering discourse where students share solutions to problems
and explain their mathematical reasoning.
Lesson Map
The teacher support materials help teachers guide instruction.
The lesson map provides recommendations like how and when
to group students for problem investigations, offers guiding
questions to assess student understanding, and provides notes
and tips regarding common student misconceptions and
errors. It also provides suggestions for closing lessons,
assigning follow-up activities, delivering assessments, and
space to record teacher reflections.
Task-Based Lessons
The lessons and activities are carefully designed to help
teachers engage students in learning mathematics. The
task-based lessons are organized by problem scenarios
and investigations. For example, a problem scenario about
tipping in a restaurant may be designed to help students
use percents. The activities may require students to convert
between fractions, decimals, and percents and consider
mathematical relationships. The real-world math tasks
motivate students to learn and help them to consider how
mathematics is a part of their daily lives.

COGNITIVE TUTOR ®
SOFTWARE FEATURES
Based on over 20 years of research into how students think and learn, the Cognitive Tutor ® Software was developed around an artificial intelligence
model that identifies weaknesses in each individual student’s mastery of mathematical concepts. It then customizes prompts to focus on areas where
the student is struggling, and sends the student to new problems that address those specific concepts.
Innovative Research-Based Pedagogy
>> Engages students directly in problem solving.
>> Uses concrete, real-world scenarios.
>> Prompts a student to think abstractly, by
converting situations into quantities and units.
Multiple Representations
>> Students work with multiple representations of
a problem.
>> The Solver encourages students to express the
problem numerically.
>> The Grapher displays the problem graphically
in a coordinate plane.
>> The Worksheet prompts students to convert
word problems to mathe matical expressions.
Interactive Examples
>> Delivers on screen, step by step instruction for
each software unit.
>> Students can see and engage in examples that
promote a conceptual understanding of the
problems being solved.

Embedded Assessment
>> Offers continuous, formative assessment
throughout the curricula.
>> Delivers pre- and post-tests that automatically
tie to custom-sequenced curricula.
>> The pretest may be configured to be diagnostic,
in which case results are used to set pacing for
students in the instructional software.
Just-in-time Feedback
>> Hints are contextual and oriented towards
helping the student to solve key steps in
the problem.
>> Immediate feedback enables the student to
self-correct and leads to more effective learning
and applying of the mathematics.
Skillometer
>> As a student becomes more proficient in a skill,
the bars on the Skillometer increase in length
and turn gold, indicating mastery.
>> Teachers can view an immediate snapshot of
each student’s progress.
>> Students receive a dynamic, strong motivator
to succeed.
Reports
>> Detailed reports document student activity in
the software, including: mastered skills, number
of problems solved, errors, help requests, etc.
>> Use data to guide instructional decision-making.

CARNEGIE LEARNING
BLENDED MATH CURRICULA
Bridge to Algebra
Carnegie Learning ® Bridge to Algebra is designed as a
pre-requisite course for Algebra I. It can be
implemented with students who lack the
fundamentals necessary for success in Algebra I, as
well as advanced middle school students.
Algebra I
Carnegie Learning ® Algebra I is designed as a firstyear
Algebra course. It can be implemented with
students at a variety of ability and grade levels.
Geometry
Carnegie Learning ® Geometry is designed to be taken
after an Algebra course. It can be implemented with
students at a variety of ability and grade levels. The
course assumes number fluency and basic algebra
skills such as equation solving.
Algebra II
Carnegie Learning ® Algebra II is designed as a secondyear
Algebra course. It can be implemented with
students at a variety of ability and grade levels. The
content in this course aligns to a model high school
math course for Algebra II and end of course exam.
Integrated Math I-III
Carnegie Learning ® Integrated Math I–III is a three
course series that weaves together numeric, algebraic,
geometric, and statistical curricula. It can be
implemented with students at a variety of ability and
grade levels.
Contact Us
To request sample materials, please visit us at
www.carnegielearning.com or contact a sales
representative at info@carnegielearning.com or
888.851.7094.
Frick Building
20th Floor
437 Grant Street
Pittsburgh, PA 15219
Toll Free: 888.851.7094
Local: 412.690.6284
Fax: 412.690.2444
info@carnegielearning.com
www.carnegielearning.com
Carnegie Learning ® , Cognitive Tutor ® and Learning by Doing ® are registered trademarks of Carnegie Learning, Inc.
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