### Inquiry, Process and Practice in the Mathematics Classroom

```INQUIRY, PROCESS AND
PRACTICE IN THE MATHEMATICS
CLASSROOM
Presented by Diane Burtchin
Rossford Schools
Diastrict Math Coach
IMPORTANT INFORMATION
 Restrooms
 Handouts
 Seating
arrangements
 Overview of the evening
OUTCOMES
 Your
 My
goals for the session
goals for the session
WHAT IS INQUIRY?
 Turn
to an elbow partner and
 What
 What
is inquiry?
does inquiry look like in the
mathematics classroom? Provide
specific examples.
INQUIRY IS…
 Inquiry-based
learning is a learning
process through questions generated from
the interests, curiosities, and
perspectives/experiences of the learner.
 When investigations grow from our own
questions, curiosities, and experiences,
learning is an organic and motivating
process that is intrinsically enjoyable.

Taken from Inquiry Learn
WHAT DOES INQUIRY LOOK
LIKE IN THE CLASSROOM?






question (or for solutions to a problem)
This results in the beginning of exploration and
hypotheses creation
These hypotheses lead to an investigation to test the
hypotheses or find answers and solutions to the
question and/or problem
The investigation leads to the creation or
construction of new knowledge based on investigation
findings
The learner discusses and reflects on this newlyacquired knowledge, which, in turn leads to more
questions and further investigation
THE MATHEMATICS CLASSROOM
 So
turn back to your elbow partner and
revisit your notes on what this looks like
in the mathematics classroom.
 Are
there any similarities between your
list and what was just mentioned?
 Does
this inquiry process remind you of
curriculum/standards?
THE PROCESS STANDARDS
 Problem
solving
 Reasoning
 Communication
 Representation
 Connection
THE PROCESS STANDARDS CONTINUED
 So
what do these mean?
 What
do they look like in the
classroom?
PROBLEM SOLVING
 The
process of determining a method for
arriving at a solution to a problem.
 This is the one we incorporate most
naturally into our instruction and practice
 Real-world applicability
 But what is the process? Is there more
than one? Does it change based on the
GOOD PROBLEM SOLVERS CAN…
 Translate
words and situations into
mathematical terms and representations
 Use/have a range of strategies and can
select the most effective strategy for a
given situation
 Can recognize when results do not make
sense, solutions do not exist, and when
results do not apply for particular
situations
 Recognize the importance of checking
solutions and know how to do so
REASONING…
 Involves
examining patterns, making
evaluating those conjectures
 Is critical in mathematics as well as other
disciplines
 Includes creating mathematical
arguments and supporting them
 Is the ability to evaluate reasoning and
problem solving processes of self and
others
THOSE WITH GOOD REASONING CAN…
Recognize patterns and categorize objects and
data, and justify answers using reasoning and
simple facts (in the earlier grades)
 Formulate conjectures and counter examples, and
apply their reasoning techniques to mathematical
ideas, concepts, and relationships (middle and
 Prove conjectures with formal inductive and
deductive arguments, evaluate their own and
others’ arguments and solutions, and make

COMMUNICATION IS…
 Being
able to explain orally and in
 Is
an essential 21st century skill in
all disciplines
STUDENTS WITH GOOD
COMMUNICATION CAN…
for mathematical meaning
 Use mathematical terms, ideas, and concepts
appropriately
 Share their own problem solving processes orally
and in writing to clarify, organize, and reflect
upon their own understanding
 Present their findings to peers and other
audiences, explain their thought processes, and
discuss how they arrived at a solution
REPRESENTATION IS…
 Symbolic
(using letters, numbers,
equations, etc.) or visual (charts,
graphs, physical objects, etc.)
 Being able to show a concept,
problem, situation, etc. in a variety
of ways
 Important to the ability to effectively
communicate
A PROFICIENT STUDENT IN
REPRESENTATION CAN…
 Use
physical objects to represent
mathematical ideas such as
fractions, decimals and percents (in
notation to show very small and very
large numbers (in the middle grades)
 Use graphs to represent
mathematical ideas both with and
without technology
CONNECTIONS…
 Making
connections between skills
and concepts within mathematics
 Making connections between
mathematical concepts and other
disciplines and the outside world
STUDENTS WHO DEMONSTRATE A
KNOWLEDGE OF CONNECTIONS CAN…
 Connect
prior learning to current learning
 Can see the importance of mathematics in
other disciplines
 Draw upon specific process skills and use
them in more complicated situations
 Take mathematical skills and apply them
in other situations (for example, reading
graphs in other subjects)
THE “NEW” MATHEMATICAL PRACTICES
Make sense of problems and persevere in solving
them
 Reason abstractly and quantitatively
 Construct viable arguments and critique the
reasoning of others
 Model with mathematics
 Use appropriate tools strategically
 Attend to precision
 Look for and make use of structure
 Look for and express regularity in repeated
reasoning

MATH PRACTICES
 So
what should each of these Practices
look like in the classroom?
 Pick
ONE practice that you feel MOST
comfortable with, turn to your elbow
Then switch.
 Repeat
for another ONE of the
Practices you feel LEAST comfortable
with.
SO ARE THESE PRACTICES REALLY
NEW?
 Complete
the envelope activity with
a partner or in a small group. Match
the “new” Mathematical Practices to
the “old” Process Standards.
 What
do you notice?
 What “stays”?
 What is “new”?
 Other thoughts?
PROCESSES VS. PRACTICES

Problem Solving
Make sense of problems and persevere in solving them
 Use appropriate tools strategically


Reasoning and Proof
Reason abstractly and quantitatively
 Look for and express regularity in repeated reasoning
 Critique the reasoning of others


Communication


Representation


Construct viable arguments
Model with Mathematics
Connections
Attend to precision
 Look for and make use of structure

SO HOW ARE WE CURRENTLY
IMPLEMENTING THE PROCESS
STANDARDS INTO OUR TEACHING?
 Share
you implement the process standards
into your teaching (how often, in what
way, your methods, assessment, level of
comfort, etc.)
IS IT ENOUGH?
 Do
 If
we need to make changes?
so, what do we need to change?
PARCC
Ohio has made a decision on the consortium it will
use for the new CCSS assessments: PARCC
 Refer to handout of an overview of the PARCC plan
 Website:
http://www.parcconline.org/parcc-content-frameworks
 Highlights: Computer-based; optional through course
computer assessment; rapid reporting system to
inform instruction and accountability
 Tossing around the idea of making them adaptive
 Starts with the content and is trying to build in the
assessment through the Mathematical Practices

BAND
 Look
through the activity selected for
following:
 How
does it tie into the idea of inquiry?
 What process standards/mathematical
activity?
 How could you modify it for classroom
use?
go to www.insidemathematics.org (do
NOT use Internet Explorer to open this…)
and click on Tools for Educators. The choose
a grade level that is closest to what you teach.
Click on MARS tasks to see a variety of rich
 Spend some time looking through these tasks
(you might want to just open the Entire
Toolkit Packet) and look for how these tasks
incorporate the ideas of inquiry and the
Mathematical Practices.
MODEL CURRICULA
 Go
to the ODE link from the COSMOS
page
http://cosmos.bgsu.edu/inquiryseries/decem
berhandouts.htm
Open up the PDF of the Model Curricula
Area. Pay particular attention to the
resources. Explore these looking for ones
that also incorporate the ideas of inquiry
and Mathematical Practices.
QUESTIONS?
 If
you have questions or need
contact me at:
[email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
 Thanks
and participation this evening!
```