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:

dburtchin@rossfordschools.org

Thanks so much for your attendance and participation this evening!