Math Investigations
is our district-adopted primary curriculum tool for mathematics
instruction Kindergarten through Fifth Grade and is proudly taught
daily in each classroom in our school. It's aim is to offer students
opportunities to explore meaningful problems in-depth to solve them
creatively and collaboratively with their peers in order to construct
personal meaning of mathematics concepts (problem solving and
concept-based learning). This approach is very different from that
of "more traditional" curriculum tools, which many adults experienced
as children and focused on applying formulas, rules, performed
procedures and algorithms (skill-based learning). Research shows that
when students develop their own ways of solving problems they retain
their understanding. When students work together with their peers to
solve problems they evaluate approaches and justify their reasoning,
leading to deeper understanding and mathematical fluency. The
mathematics teachers in our school, through several years of teaching Math
Investigations, have observed a series of "typical" non-routine
approaches used by our students when approaching problems
presented during the Math Workshop which are grounded in their
developing understanding of our number system. Some of these
approaches are introduced and nurtured through the Investigations
curriculum and others are developed simply through student
exploration. The following link will connect you to a site which
illustrates these strategies so that you may gain a better
understanding of the approaches we are using with addition,
subtraction, multiplication, and division of whole numbers.
Click here for
videos explaining
Math Strategies
Solving a Word Problem
A Complete Solution to a Word Problem
includes: a written estimate, all the work that you do, an equation (even
if you solved it using column form), a diagram, number line, chart or
other representation, and the answer to the question in a complete
sentence.
What if I get stuck? If you get
stuck you can: look at past lessons, look at the charts that are posted
in the classroom, try the problem using counters or other materials,
sketch a diagram or other representation, change the numbers to make the
problem simpler, write what you do know, write down questions to ask
later, or check other resources.
Frequently Asked Questions
Why are Investigations being used to teach my child mathematics?
This curriculum
gives children different ways to express their thinking. After being given
situations for problem-solving, students develop strategies for expressing
mathematics, allowing ownership of understanding. Through working with
peers, students justify and analyze solutions. As a result, they are able
to understand important relationships between concepts.
How are Math
Investigations different from traditional math approaches?
Through Investigations, children
develop personal meaning of concepts and learn to reason mathematically.
They are not taught to rely on set procedures, formulas and rules that
may have no meaning to them. The same concepts are covered as those in
traditional textbooks, only the approach is different. Research shows
that students who construct math for themselves are going to gain fluency
and remember what they have learned. They will also keep trying to make
sense of problems.
How will Math
Investigations affect my child?
Your child will learn to be a
self-directed learner with the ability to approach unfamiliar problems and
develop ways to solve them. Your child will also develop communication
skills about mathematics, learning to use, represent and explain concepts.
Instead of the teacher being the sole authority for answers, each child
will learn to rely on logic and mathematical evidence as verification of
understanding, becoming a confident learner of mathematics!
How can I help my child at
home and what should my child use to study from?
Students should review daily
activities to reflect on their understanding by discussing classroom
experiences with you. Your child may reflect on conversations from the
Math Workshop, or possibly show you some of the strategies that the class
has used to solve particular problems. Homework will also be assigned
regularly to reinforce learning in the classroom. When student sheets
are assigned as homework, parent notes and tips will be provided on the
back to help you in working with your child.
Why are there no student
textbooks? Textbooks do
not come with this curriculum. Instead of learning math through a book,
children are actively engaged in mathematics through conversations with
peers and working with manipulative materials. Student sheets are used
regularly, containing problems to solve and games to play to deepen
understanding of concepts learned in the units.
How is the class period
run during the math workshop?The
math workshop contains three parts: opening meeting,
work period, closing meeting
During the opening meeting, your child’s teacher explains the goals
for the math workshop and teaches a mini-lesson, introducing a new concept
or skill. The teacher then poses a problem or series of problems for each
child to solve based on the conversation during the mini-lesson.
During the work period, your child works individually, with a peer
or with a group, to solve the problem(s) presented in the mini-lesson,
developing ideas and strategies. The teacher facilitates learning by
circulating around the room, working/conferencing with students
individually or in small groups.
During the closing meeting, the class regroups to discuss strategies
used to solve the day’s problem(s), to share misunderstandings and correct
them, to make connections to other areas of math and the real world, and
to reflect on what was learned during the lesson. Following this, homework
is usually assigned to reinforce and extend what was learned during the
day.
Are the children learning
the basic skills? Yes.
With experience, each child will learn to remember basic skills by
constructing sense of them. Although fluency is more important than
memorization, occasional drill and review exercises occur during the
mathematics workshop to create balance of learning.
Why is there so much
written work? One of the
main goals of standards-based education as well as Investigations is for
students to be able to confidently communicate about mathematics. In order
for a child to truly understand a concept, he/she must be able to use,
represent, and explain his/her thinking of the mathematics. Communicating
about math gives children ownership over their understanding.
Can I observe a
mathematics lesson with my child’s teacher?
Absolutely. Simply write a note or
make a phone call to your child’s math teacher to schedule a time
convenient for both of you. Math is taught each day during a full
one-hour workshop.
How do absences
affect my child?
When your child is
absent, it is extremely difficult to make up work because mini-lessons and
communication that take place during the math workshop are missed. Many
lessons also relate in Investigations, therefore, when a child is absent
he/she does not see connections being made, and as a result, has a harder
time participating in class discussions. It is important to limit absences
to a minimum so that your child may gain a complete understanding of
concepts being explored in the classroom.
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