# MVP Curriculum Philosophy

The Mathematics Vision Project

“The most necessary task of civilization is to teach people how to think. It

should be the primary purpose of our public schools . . . The trouble with our

way of educating is that it does not give elasticity to the mind. It casts the

brain into a mold. It insists that the child must accept. It does not encourage

original thought or reasoning, and it lays more stress on memory than

observation.” Thomas A. Edison

The Mathematics Vision Project (MVP) was created as a resource to teachers who desire to implement the Common Core

State Standards (CCSS) using a task-‐based approach that leads to skill and efficiency in mathematics by first developing

understanding. The MVP approach is neither purely constructivist nor purely traditional. Rather, the approach takes

seriously the Standards of Mathematical Practice and develops these practices through experiential learning in mathematics. Students engage in mathematical problem solving, guided by skilled

teachers,

with

the

desired

outcome

that

students

will

achieve

mathematics

proficiency

as

defined

in

Adding

It

Up—conceptual

understanding,

procedural

fluency,

strategic

competence,

adaptive

reasoning,

and

productive

disposition.

(Adding

It

Up,

p.

5)

The

authors

have

taken

on

the

challenge

made

by

the

National

Research

Council

to

create

a

curriculum

where

students

do

not

learn

solely

by

either

“internalizing

what

a

teacher

or

book

says

or,

on

the

other

hand,

solely

by

inventing

mathematics

on

their

own”

(Adding

It

Up,

p.

11)

In

this

way,

all

the

strands

are

developed

in

a

balanced

way

and

students

achieve

proficiency.

The

Mathematics

Vision

Project

is

committed

to

helping

educators

implement

the

Common

Core

State

Standards

(CCSS)

as

part

of

a

continuum

of

mathematics

instruction

addressing

conceptual,

procedural,

and

representational

thinking;

depth

of

knowledge;

and

assessment.

The

CCSS

provide

a

coherent

trajectory

of

mathematical

content

that

students

should

be

learning

as

they

progress

from

kindergarten

to

12th

grade.

This

trajectory

was

developed

from

“research-‐based

learning

progressions

detailing

what

is

known

today

about

how

students’

mathematical

knowledge,

skill,

and

understanding

develop

over

time.”(CCSS,

p.4)

The

Standards

are

not

just

a

checklist

of

sequential

content

that

should

be

taught

beginning

in

grade

school

and

brought

to

a

close

in

high

school.

In

order

to

bring

the

vision

of

the

Standards

to

life,

instructional

practice

must

change.

The

MVP

method

embraces

a

different

way

for

teachers

to

organize

instruction

to

deepen

student

learning

of

mathematics.

The

MVP

classroom

experience

begins

by

confronting

students

with

an

engaging

problem

and

then

allows

them

to

grapple

with

solving

it.

As

students’

ideas

emerge,

take

form,

and

are

shared,

the

teacher

orchestrates

the

student

discussions

and

explorations

towards

a

focused

mathematical

goal.

As

conjectures

are

made

and

explored,

teachers

use

formative

assessment

to

guide

students

as

they

embrace

effective

strategies

for

analyzing

and

solving

problems.

Students

justify

their

own

thinking

while

clarifying,

describing,

comparing,

and

questioning

the

thinking

of

others

leading

to

refined

thinking

and

mathematical

fluency.

What

begin

as

ideas

become

concepts

which

lead

to

formal,

traditional

mathematical

definitions

and

properties.

Strategies

become

algorithms

that

lead

to

procedures

supporting

efficiency

and

consistency.

Representations

become

tools

of

communication

which

are

formalized

as

mathematical

models.

This

is

how

students

learn

mathematics.

They

learn

by

doing

mathematics.

They

learn

by

verbalizing

the

way

they

see

the

mathematical

ideas

connect

and

by

listening

to

how

their

peers

perceived

the

problem.

This

process

describes

the

Continuum

of

Mathematical

Understanding

and

it

informs

how

teaching

should

be

conducted

within

the

classroom.

Each

module

in

the

MVP

educational

program

has

been

carefully

designed

and

sequenced

with

rich

mathematical

tasks

that

have

been

formulated

to

generate

and

develop

the

mathematical

concepts

within

the

core.

Careful

attention

has

been

placed

upon

the

way

mathematical

knowledge

emerges.

Some

tasks

are

developmental

tasks

while

others

are

for

solidifying

or

practicing

the

concepts.

The

tasks

also

encourage

students

to

notice

relationships

and

make

connections

between

the

concepts.

In

this

way,

students

perceive

mathematics

as

a

coherent

whole.

While

the

classroom

experience

begins

by

improving

students’

reasoning

and

sense-‐making

skills,

it

does

not

conclude

until

mathematical

understanding

becomes

procedural

skill

as

evidenced

through

application.

Hence,

the

Ready,

Set,

Go!

homework

assignments

are

focused

on

students

practicing

procedural

skills

and

organizing

principles

to

add

structure

to

the

ideas

developed

during

the

classroom

experience.

As

in

any

discipline,

practice

is

the

refining

element

that

brings

fluency

and

agility

to

the

skills

of

the

participant.

Together

the

classroom

experience

and

the

Ready,

Set,

Go!

homework

assignments

present

a

balanced

combination

of

procedure

and

understanding

for

the

student

practitioner.

The

Mathematics

Vision

Project

has

produced

the

first

high

school

textbook

to

outline

the

steps

a

practicing

teacher

can

take

to

faithfully

implement

the

Integrated

Pathway

Secondary

Mathematics

1

core

standards.

The

modules

have

been

carefully

crafted

and

sequenced

to

allow

the

specific

mathematical

ideas

identified

in

the

core

to

surface

and

then

flourish

into

rich

mathematical

knowledge

and

skill

for

all

students.

The

textbook

for

Integrated

Pathway

Secondary

Mathematics

1

assumes

that

students

enrolled

in

the

course

have

been

properly

prepared.

The

Getting

Ready

module

may

be

used

in

the

classroom

to

review

content

that

should

have

been

mastered

in

previous

course

work

but

is

also

necessary

for

success

with

the

new

material.

The

Ready,

Set,

Go!

homework

assignments

have

been

designed

to

continue

to

spiral

a

review

of

content.

Combined,

the

classroom

experience

and

the

Ready,

Set,

Go!

homework

assignments

offer

a

powerful

blend

of

new

learning

and

maintained

proficiency.

For

more

information

about

the

Learning

Cycle

follow

the

link.

http://edutech.csun.edu/trd/sites/edutech.csun.edu.rtcweb/files/CMI%20Article.doc.

For

more

information

about

the

Mathematics

Vision

Project

visit.

www.mathematicsvisionproject.com