Planning for Implementation
should be given to many issues as you study the Core-Plus Mathematics program
and plan for an effective implementation of the program. Excerpted
below are a selection of entries from Implementing Core-Plus Mathematics (the full document is available
for download). You may wish to access
resources related to improving mathematics education from organizations
such as the Mathematics Assessment Resource Service (MARS) "Resources
for Leaders in Mathematics" (toolkitforchange.org).
the CPMP Program
Spend time developing
goals for your mathematics program that align with various recommendations
such as NCTM's Principals and Standards for School Mathematics (NCTM,
2000), NCTM's Focus in High School Mathematics, the College
Board Standards for College Success: Mathematics and Statistics (2006),
the American Diploma Project Standards, and your state mathematics
recommendations. This work should involve representatives from
all stake-holders in the district. All high school mathematics
teachers should be involved at each step of the goal-setting process.
of your mathematics program goals and a support base from administrators,
counselors, parents, board members, business/ community leaders,
other departments within your high school and middle school faculty.
Form a curriculum
study committee to align your district's mathematics program goals
across grades K-12. One valuable resource is Choosing a Standards-based
Curriculum from the Educational Development Center (EDC: www2.edc.org/mcc/pubs/mguide.asp).
study the Core-Plus Mathematics materials and instructional
model as well as other programs. Consider reviewing mathematics
programs with high-quality research on student achievement. Curriculum
should be seen as a tool to move toward your district mathematics
technology needs. A graphing calculator with statistics capabilities
such as the TI-84 is required for each student. Some districts
provide an at-home calculator for each student, as well as an in-class
set for each mathematics teacher. The free public-domain software CPMP-Tools has
been developed to support student learning and technology needs
at home and at school.
Create an extended
professional development plan that will provide ongoing support
for high school, middle school, and special education teachers.
Information on course-specific CPMP implementation workshops is
available from Glencoe/McGraw-Hill and under Implementation.
On-site professional development programs can be designed to meet
cooperative learning, technology, literacy, and alternative assessment
workshop opportunities for mathematics teachers before they attend
curriculum implementation workshops or begin teaching the curriculum.
with Course 1 and add a course level each year. Encourage
teachers to progress from Course 1 to Course 4 in stages,
so they can develop an understanding of the growth of mathematical
ideas across the curriculum.
to allow for common planning periods for teachers teaching the
Formulate a plan
to evaluate your mathematics program and the results of changes
made. Plan to collect data over the long term, not just the year
or two before and the year or two after the changes. (See examples
Produce a Frequently
Asked Questions document containing your district's responses to
local questions so that there are common responses from administrators,
mathematics teachers, counselors, science teachers, and school
district and individual teacher decisions can affect the amount
of material taught each year. In particular, time should be spent
aligning middle and high school mathematics programs to maximize
to align with your state mathematics standards and to polish skills
using the practice sets and review tasks in each lesson and the
practice sets available in the Unit Resource Masters.
for instructional leaders, particularly building principals, to
understand the goals of the mathematics program and discuss ways
to promote effective classroom instruction. One professional development
option for teams from the school is the Lenses on Learning courses
offered by the Educational Development Center. See www2.edc.org/CDT/cdt/cdt_lol1.html.
If your district
has a history of enrolling strong eighth-grade students in an algebra
course, you may wish to maintain an accelerated program using Core-Plus
Mathematics Course 1 for select eighth-graders. These students
could then enroll in AP Calculus as seniors upon completing Course 4
as juniors. Students can enroll in AP Statistics anytime after completion
of Course 3.
Consider ways to schedule classes to allow
for individual students to accelerate themselves. The following is a
list of options that some districts implementing Core-Plus Mathematics have
successfully used in cases in which accelerated students have not studied
Course 1 as eighth-graders. Acceleration models employed by CPMP
schools to allow enrollment in Advanced Placement Calculus or Statistics
include the following.
Mathematics Course 1 in middle school for selected eighth
students enrolled in the grade level mathematics course additional
mathematics material from Core-Plus Mathematics Course 1
that will allow them to enroll in Course 2 in ninth grade.
This can be done during the academic year or in a summer program.
ninth graders who have completed one of the NSF-funded middle school
mathematics programs, or an algebra course, could be enrolled in
Course 2. Prerequisite material from Course 1 can be
distributed throughout the school year as needed for particular
Course 2 units or taught in a summer course.
In schools with
semester block scheduling, a student could enroll in two courses
in a given year.
In schools with alternate-day academic-year
block schedules, the schedule could be adjusted for one or more
classes of a course to meet each day for the entire school
year, thus covering two of Courses 1-4 that year.
In schools with
academic-year schedules, two mathematics classes may be scheduled
back-to-back to allow study of one course in the first semester
and the next course the second semester.
A student could
choose to double up on classes as a senior by enrolling in both
Course 4 and AP Statistics.
Equity, and Differentiation
One question frequently
asked by districts adopting Core-Plus Mathematics is related to
equity and approaches to accommodate the program for special-needs students.
Several research studies have provided
evidence that introducing activities through class discussion, teaching
students to explain and justify, and making real-world contexts accessible
to students promote greater access and equity in mathematics classrooms.
(Boaler, J. "Learning from Teaching: Exploring the Relationship Between
Reform Curriculum and Equity," Journal for Research in Mathematics
Education, 2002, Vol. 33, No. 4, 239-258, and Brown, C.A., Stein,
M.K., and Forman, E. A. "Assisting Teachers and Students to Reform Their
Mathematics Classroom," Educational Studies in Mathematics, 1996,
31-93). Practices that help promote equity are briefly discussed below.
Through Class Discussions Group and class discussions of the
aim of investigations, the meaning of contexts, the challenging points
within problems, and possible problem access points to which students
might turn make tasks more evenly accessible to all students.
to Explain and Justify their Thinking Giving explicit attention
to explaining thinking and evaluating what makes a good piece of
work helps students improve their work.
Contexts Accessible Considering the constraints that real situations
involve and connecting these situations with issues and topics in
their own lives helps students view mathematics as something that
will help them interpret their world.
that Promote Equity Mixed-ability classes, a focus on problems
solving, high expectations for all students, attention to a broad
array of mathematical topics, and allowing students to restate problems
in their own words also appear to help students from different racial,
ethnic, and linguistic groups be more successful in mathematics.
Core-Plus Mathematics offers many
opportunities for teachers to incorporate these practices into daily
routines. One such built-in opportunity is the Think About This Situations
(TATS) used to introduce lessons through discussions. Although no TATS
questions are in the student text for individual investigations there
are often suggestions in the Teacher's Guide for class launches
of investigations. Since much of the mathematical content is based on
real contexts, it is important that all students understand the contexts
and draw on their own or a classmates background knowledge. Opportunities
for students to explain and justify their thinking are built into all
curriculum features. Look for opportunities to encourage the habit of
mind of justifying their thinking, individually and in small group or
In addition, in the Teacher's Guide periodically,
notes provide specific ideas for differentiation. Look for DIFFERENTIATION margin
notes and student masters.
It is important to recognize that implementing
the Core-Plus Mathematics curriculum with classes consisting only of
students previously unsuccessful in mathematics will create additional
implementation challenges. These classes should not be expected to complete
all units from a CPMP course.
Some schools provide special-needs students
with a second hour of class devoted to support. This class typically
follows the regular mathematics class. During this class time, students
are assisted with their homework and sometimes pre-read material for
the next day's class period. This support for special-needs students
increases the access to the mathematics content during the regular class
As one special education teacher indicated:
"I have been teaching the CPMP in a resource setting for the past
2 years and have been teaching mathematics in the resource setting
for over 8 years. I have to admit that initially I was adamant
that my students (the majority have specific learning disabilities
either with respect to math or reading) would be incapable of using
this program. After 2 years, I have found that the opposite is true.
My students are more engaged and achieving
higher-level concepts because of CPMP. We do move at a slower pace,
but they are learning the concepts of Algebra and Geometry thanks to
the contextual component and the guided discovery approach. The program
also provides ample opportunities to differentiate instruction. I am
fortunate to work in a district where the staff received excellent
training and we have access to technology. Overall, the students are
doing well. I am looking forward to the training for Course 3.
Mathematics is definitively a program that works well for students
with learning disabilities."
For review copies
of Courses 1,
2, 3, and 4 (Preparation for Calculus) student and teacher
materials, contact your McGraw-Hill representative. You may wish
to request the CCSS Guide to Core-Plus Mathematics and the Implementing
Core-Plus Mathematics guide to aid in your review and/or implementation
of the program.