Many individuals from my generation have childhood memories
of retrieving an encyclopedia off of the shelf to write a school report, having only three television stations, being restricted to a single room
while talking on the phone (due to the cord), and our experiences learning
math. I recall my math teachers
demonstrating a procedure as “the” method for solving a particular type of
problem. All I had to do was memorize the
steps through repetitive practice. I
remember working what seemed to be fifty or more similar problems, only to get
to the end of the page where the dreaded word problems were. The good thing about these word problems was
that I knew I would be practicing that same procedure, so I just needed to pull
the numbers from the problem and go through the steps. I became really good at memorizing procedures
and getting correct answers, without even breaking a sweat. The reality was that I was not afforded the
opportunity to make sense of the mathematics.
Mathematics
in the 21st Century
Math instruction has changed dramatically in the 21st
century. The ability to perform basic
calculations is no longer the primary goal.
In this age of technological advances, computers can perform these
routine math tasks. In order to prepare
our children for success in the 21st century workforce they will
need a conceptual understanding (understanding/insight of mathematical
concepts) as well as procedural fluency (skill in
carrying out procedures flexibly, accurately, and efficiently). It will be necessary for them to understand
when, why, and how to apply this knowledge to solve unconventional, real-world
problems. Simply put, students are being
asked to think deeply and create meaning with mathematics.
The Partnership for 21st Century Skills (Framework for 21st Century Learning, 2014), founded in 2002,
began as a coalition of business leaders, educators, and policymakers. Extensive research was conducted identifying
the knowledge and skills necessary for success in our global, 21st
century world. It is the mission of the
Partnership for 21st Century Skills that our students obtain these
skills, and this can be accomplished by fusing four crucial skills with the
content areas of reading, writing, and mathematics. These skills are more commonly known as the
4Cs.
- Critical thinking/problem
solving
- Communication (written and oral)
- Collaboration
- Creativity/innovation
Mathematics is
the key to developing the 21st century skills our children need, and
utilizing these skills is the key to their understanding of mathematics.
Math
Achievement in the United States
The research shows that historically, tremendous learning
gaps have existed with American students in the area of mathematics. A high percentage of college freshman have
had to take remedial math courses. There
have been serious deficiencies with the math achievement of our students,
compared to students in other countries. The US ranked 37th in the
world on the 2012 PISA mathematics assessment (Programme for International Student Assessment,
2012).
This is concerning because, our children will be competing for opportunities in
a global economy. In order to prepare
our students we must continue to raise the bar and provide a more rigorous
curriculum.
What
does this mean for students in our math classrooms?
Math instruction at Paine Intermediate is founded on
research-based best practices. The
National Council of Teachers of Mathematics (NCTM), The National Science
Foundation (NSF), and other key organizations, have conducted a decade or more
of extensive research on the most effective instructional practices in
mathematics. The following are key
components of our math curriculum.
- We introduce new concepts through rigorous
investigative tasks, where students have opportunities to construct conceptual
knowledge. These tasks have multiple
entry points and a variety of solutions strategies, allowing students at all
levels to build on their previous knowledge. Students will use mathematical representations
to deepen conceptual understanding.
- Students will engage in conversations regarding
their problem solving approaches and construct arguments to defend their
solution strategies.
- We conduct daily mental math number talks to
promote flexibility with numbers and numerical reasoning.
- Our students will develop procedural fluency
once they have formed a conceptual understanding.
- Teachers will provide direct instruction in the
form of mini-lessons at strategic points during a unit to cement concepts,
procedures and math terminology.
- Throughout the unit, the teacher is asking
meaningful questions to assess student understanding and to advance their
mathematical reasoning.
- Students are provided with opportunities to
apply and extend their learning through a math menu of activities. The menu is comprised of tasks at various
levels, where students are able to make choices based on their current
knowledge base.
- Teachers are constantly assessing student
understanding through quick formative assessments, independent performance
tasks where students apply what they have learned in a different context, and
end of unit assessments.
- We utilize DreamBox learning as a supplement to
our math curriculum. This program
provides students with opportunities to deepen conceptual understanding and
develop numerical reasoning, as well as flexibility with numbers.
Our instructional practices promote the development of
conceptual understanding of mathematics, procedural fluency, and the development
of those crucial 21st century skills.
Parent Information
The 21st century math classroom looks different
from the one most adults experienced in the past. We know this can be frustrating for many
parents, because it is unclear on how to best support your child at home. We
are sensitive to this, and are hopeful this blog, and other communications that
we plan to implement this year, will lessen any confusion. The NCTM website contains a parent resource page containing tips for how to best help your child at home. They recommend asking your child questions
while they are working on a problem rather than showing them how you would do
it. Questions may include: what are you being asked to find out, can you
describe what the problem is telling you in your own words, is there a part
that you already know how to do, will it help to make a list, chart, or table,
etc. They also suggest that parents work
with their children on fact fluency at home once basic facts have been taught
at school. The NCTM website also offers other information for parents on their website. Click on the following link for the family
resource page (National Council of Teachers of Mathematics, 2014). http://www.nctm.org/resources/families.aspx
In closing, this post is intended to provide an overview of
why math instruction has changed. Additional
information will be provided throughout the year via this blog. We hope this will be useful to parents. We
will highlight some of the exciting learning that is occurring in our math
classrooms. We will also be preparing
short video clips for parents on various strategies your children are using at
school. There is much more to come! Our goal is to create mathematical problem
solvers who are knowledgeable and confident.
If we can be of any assistance, please let us know.
Sources
Family Resources. (2014). Retrieved from National Council of Teachers of Mathematics:
http://www.nctm.org/resources/families.aspx
Framework for 21st Century Learning. (2014). Retrieved from Partnership for 21st Century Skills:
http://www.p21.org/
Programme for International Student Assessment. (2012). Retrieved from
http://www.oecd.org/pisa/keyfindings/PISA-2012-results-US.pdf
