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INQUIRY, PROCESS AND PRACTICE IN THE MATHEMATICS CLASSROOMPresented by Diane Burtchin
Rossford Schools
Diastrict Math Coach
IMPORTANT INFORMATIONRestroomsHandoutsSeating arrangementsOverview of the evening
OUTCOMESYour goals for the session
My goals for the session
WHAT IS INQUIRY?Turn to an elbow partner and
answer the following:
What is inquiry?
What 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? The learner asks questions These questions lead to the desire for answers to
the 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 newly-acquired 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 anything regarding your mathematics curriculum/standards?
THE PROCESS STANDARDSProblem solvingReasoningCommunicationRepresentationConnection
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 grade level of the student?
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
conjectures about generalizations, and 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 later grades)
Prove conjectures with formal inductive and deductive arguments, evaluate their own and others’ arguments and solutions, and make decisions (later grades)
COMMUNICATION IS…Being able to explain orally and in
writing about mathematical concepts
Is an essential 21st century skill in all disciplines
STUDENTS WITH GOOD COMMUNICATION CAN…
Read 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 the younger grades) and scientific 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 PRACTICESSo what should each of these Practices
look like in the classroom?
Pick ONE practice that you feel MOST comfortable with, turn to your elbow partner, and share your response. 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 Construct viable arguments
Representation 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 with your grade-band group how you implement the process standards into your teaching (how often, in what way, your methods, assessment, level of comfort, etc.)
IS IT ENOUGH?Do we need to make changes?
If 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 assessments; performance tasks prior to 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
ACTIVITY EXPLORATION BY GRADE BANDLook through the activity selected for
your grade band. Discuss the following:
How does it tie into the idea of inquiry?What process standards/mathematical
practices are addressed by this activity?
How could you modify it for classroom use?
RICH TASK SEARCH Please 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 tasks for that grade level.
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
pagehttp://cosmos.bgsu.edu/inquiryseries/decemberhandouts.htm
Open up the PDF of the Model Curricula and go to your grade level or Content 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
additional information, please contact me at:
Thanks so much for your attendance and participation this evening!