What's Up with Investigations Math?
-Frequently Asked Questions by Parents-
As you know, the Danvers elementary schools are using a new math curriculum called Investigations. It is a research-based program that emphasizes mathematical reasoning and real-life application. It represents a major shift in the way we expect teachers to teach, and children to learn. PACE offers parents these FAQs in an effort to continue education and dialogue concerning our new curriculum.
Q: What was wrong with the old ways that we taught math? Why do we need to change our program?
There are a number of reasons
that Danvers—along
with many other schools in Massachusetts and the
nation—saw
a need to change its mathematics program.
One
reason is that the traditional ways of teaching math have simply become
outdated. Over the past 20
years
or so, our economy—and real-life demands for
math—have changed radically, while instruction in schools has not. Mere arithmetic proficiency (the old
way) worked for some of us, but it is no longer sufficient for
todayÕs
students. Today, our kids need
more real-life application skills that come from a strong background in
mathematical reasoning and problem solving skills.
Another
reason is that we need to incorporate new learning research into our
math
instruction. With the old ways, we used a one-size-fits-all method,
never
considering how children
best
learn math.
The new research-based curriculum gives us more effective
teaching methods to address more learning styles and give more children
the
opportunity to demonstrate their potential. The
new curricula, like Investigations, meet the needs of all types of students:
from gifted,
to those functioning below grade level, to the various groups in
between. Programs like ours also reduce
ethnic,
socioeconomic and gender gaps.
Furthermore,
we need a change because the United States consistently scores lower
than other
developed nations on tests of math reasoning and problem solving. International comparative studies
indicate that our old ways of teaching math do not help students learn
concepts
in depth.
Instead, they encourage students to
learn procedural skills, in a passive classroom routine that involves
only
listening and note taking.
Currently, the average
students in other countries know as much math as our top students!
How have they done this?
They have taught math that in a way that emphasizes depth over
breadth. This is what our new
curricula will do for us.
Lastly,
our old ways of teaching math dashed the confidence of many students.
If it
worked for you, consider yourself fortunate, because many adults today
still
sadly lack confidence in math, or proclaim that theyÕre
Ònot good at it.Ó Why is
this? It is because old ways of
teaching did not meet the needs of many students. With
todayÕs curricula, more learning styles are addressed,
and students have more opportunity to internalize math in a way that
makes
sense to them. They end up better
equipped to tackle new challenges.
Many
other districts in MA are using Investigations. For a
list of some of them, please see www.lab.brown.edu/investigations/who-implementing.
Q: How do we know that Investigations works? Is this some sort of an experiment for Danvers?
No, Investigations is not any kind of
Òexperiment.Ó It was
developed by TERC, a
well-known educational research firm based in
Cambridge, Massachusetts. We know
it works because it has been tested nation-wide for many years. Students who have used it for a number
of years have shown good improvement in their reasoning and problem
solving
skills, and more of them profess confidence in math.
Furthermore, Investigations has proved effective in various schools
settings, from
inner-city populations, to more affluent, high-achieving towns. Specifically, data has shown that kids
do better with their computation of larger numbers, their mathematical
reasoning & problem-solving, and their real-life application of
skills. This has also been
supported on state-wide tests, once programs are fully implemented. For more information on TERCÕs
research, please visit http://investigations.terc.edu/research/index.cfm
Q: What does this mean for MCAS?
The recent fourth-grade MCAS
results were the result
of only one year of
Investigations
math. It is important to know that
some gaps are fully expected during the implementation of any new
program; this is generally
referred to as an Òimplementation
dip.Ó Sometimes, an implementation
dip is reflected in test scores.
In Danvers, we are undergoing three major shifts that probably
affected
test scores:
Teachers: Teachers are
learning a different way
of teaching math! They are no
longer the ÒimpartersÓ of knowledge, with the students
following along. Now, teachers must
facilitate student
learning, allowing kids a much more active role in their learning. This represents a major shift from the
way most teachers were trained and have practiced up until now.
Students: Students are no
longer only required to
memorize facts and procedures.
They are now being asked to think in new ways, and to discuss
mathematical procedures to show understanding. They
are even asked to write about their mathematical
thinking, which proves challenging for many.
In short, they are taking a more active role in
their learning that, up until now, has not always been required.
Parents: Parents, too, need
time to learn about
the new ways of teaching and learning.
We have had to learn new ways to support our kids at home. Much of the homework looks different:
games, writing assignments, shorter assessments, less emphasis on
memorization
of facts, etc. It is all part of
an effective and well-rounded program, but it is challenging
nonetheless.
In short, full and
fluent
implementation of the program will take several years.
But we have accomplished much so
far. The Investigations program will be ever-evolving, with Danvers
faculty
constantly refining it so that it best meets the needs of our students.
Q: What will we do to improve math test scores?
We need to continue
to work
toward full implementation of the program. Student
improvement will come as we learn how to use it most
effectively in Danvers. In the
meantime, the district is continuing to work proactively.
Currently, the
district is
using its Investigations
Leadership Team to analyze MCAS math results from the last few years. This team includes at least 2 teachers
from each school. They will
analyze data and put together resources for teachers that will help to
reinforce the program. For
example, this team will develop resources for additional math practice,
MCAS
practice questions, and make sure that our program vocabulary matches
that of
the MCAS test. The team will also
determine the sequence of math units that works best for Danvers.
It is important
to
remember that Danvers continues to do well overall on the MCAS tests. This is
significant, considering that MA has some of the most rigorous testing
in the
nation. Fourth graders in MA are
ranked first in the nation, in both math and English language arts. For more information on this, please
see the National Assessment of Educational Progress website, www.nationsreportcard.gov.
Q: But I am still concerned about my childÕs knowledge of basic facts. He doesnÕt seem to have memorized them the way I did.
You are right. Your child is not spending as much time
memorizing in class. Remember: we
are striving for depth of understanding, as opposed to mere
memorization. However, if you look
carefully at your
childÕs assignments, you will see that a great deal of time is
spent focusing
on the concepts behind
the basic
operations, and the procedures s/he can use to find the answers.
If you want to help
your
child become more automatic with facts, feel free to work on this at
home. The Array Cards can be used as flash
cards and will match what is being done in the Investigations program.
In fact, many teachers do
work on automaticity in school; it is just not the main thrust of the
program. And, as we move toward
full implementation, we will find a balance of methods that works for
us. For more information about Array
Cards,
please visit this link: http://www2.lab.brown.edu/investigations/author/q40.html
.
Q: Will this new program prepare my child for Middle School? IÕve heard they donÕt use Investigations there.
Investigations will most certainly prepare your child for
middle school. In fact, the Middle School
is currently
implementing a very similar program called, Connected Mathematics. Connected Math has the same philosophical base, with an
emphasis on
math reasoning, problem solving, and application. And,
like Investigations,
skills are spiraled from year-to-year, so that
students are not learning in isolated strands that are never re-visited. Instead, skills are taught more
in-depth, with more connections and reinforcement each year.
Q: How Can I Best Help My Child?
As parents, there
are many
things we can do.
The first is as
simple as
speaking positively about math to your child. Because
the old ways of teaching have left many of us insecure
about our math skills, it is easy to unintentionally convey low
expectations to
our children. To combat this, we
need to communicate enthusiasm about math, integrate it into our
everyday
lives, and consistently encourage and praise our childrenÕs
skills.
To help with
homework—which sometimes looks foreign to us—we can:
-
Be sure that
we have
read the background that the teacher has provided for us;
-
See if we
can see
patterns in the work our children are bringing home;
-
Ask probing
questions of
our kids when tackling homework:
o
What is the
problem
youÕre working on?
o
What did the
teacher
tell you to do? Or, what do the directions say?
o
What do you
understand? What donÕt you
understand?
o
Are there
words or
directions you are uncertain about?
o
Where do you
think you
should begin?
o
What do you
already know
that might help?
o
Can you draw
a picture
or make a table to work it out?
o
LetÕs talk through some steps, and see
if we canÕt Òtalk it out.Ó
Remember that it
is o.k.
to struggle with math problems! Through trial and error, children
learn valuable skills.
If you are
struggling with
homework longer than is reasonable, simply jot a note to the teacher
about the
problem you had. He or she will
address it the next day with the child, and even write you back if
necessary.
We can also learn
more about
the Investigations program. We can attend informational meetings,
and communicate with teachers when we donÕt understand something. In fact, dialogue is the most important
tool we have!
For additional questions or comments about
Investigations Math, please contact:
Mary
Wermers, Math & Science
Curriculum Director
978-777-8932
For additional information about PACE,
please
contact:
Danvers
Public Schools
Office
of the Superintendent
978-777-4539