webinar handout - developing student understanding in mathematics

8/7/2019 Webinar Handout - Developing Student Understanding in Mathematics

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EBINARHAN

DOUT

The Mathematics Improvement Toolkit and this webinar series are supported through the U.S. Department of Education

Grant No. S332B060005, Comprehensive School Reform Quality Initiative to the National Forum to Accelerate Middle

Grades Reform and the various partner organizations of that project. More information athttp://www.middlegrademath.org

FOR MORE INFORMATION ABOUT THIS WEBINAR OR TOOLKIT RESOURCES:

http://www.middlegradesmath.org/webinar

DEVELOPING STUDENT UNDERSTANDING OF MATHEMATICS

his handout is a

upplement to the webinarn Developing Student

nderstanding of

athematics for the Middle

tart Online tools of the

olkit.


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THE MIDDLE START ONLINE PROFESSIONAL DEVELOPMENT PROGRAM

Middle Start is one of four partners, along with the National Forum to AccelerateMiddle Grades Reform, who are developing a set of support resources for

educators to address mathematics instruction for specific populations. In particular,

we are trying to address the needs of rural educators who may not have access to

quality professional development programs that focus on content and instruction to

ensure deep understanding of mathematics concepts for students. In addition, we

are drawing upon our strengths to provide resources to focus on and improve

family engagement in students learning of mathematics.

To provide access to these learning opportunities, we are incorporating Internettechnologies to allow educators from a variety of locations and schools to

collaborate online with trained facilitators to focus on key issues in mathematics

learning and instruction. Our primary focus is to ensure that classrooms provide

opportunities for all students to develop a deep conceptual knowledge of

mathematics. Too often, resources and instruction for middle grades students

reduces the mathematics curriculum to simple computational work and use of

algorithms, rather than building a deep understanding of concepts which will serve

students as learners for years to come.

The online learning tools provide a variety of resources and strategies to help

teachers examine and improve different aspects of mathematics instruction,

including selection and use of materials, recognition of common misconceptions

and the instructional practices that address this, and deepening of the teachers

own understanding of the mathematics. While we use electronic resources to allow

teachers in remote locations or with difficult schedules to access these materials

wherever and whenever they need, we also recognize the potential of peer

collaboration and ongoing learning programs to support teacher learning best. Our

approach focuses on guided collaboration with peers using these online tools thatis fostered by experienced instructional coaches and facilitators.


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ABOUT THE MATHEMATICS RESOURCES

The professional development efforts for our resources are focused primarily to address

research findings that examined issues pertinent to mathematics instruction and learning.

Some of the key findings that we are addressing include the following:

Students are rarely exposed to resources or instruction that develop conceptual

understanding and higher-order thinking skills.

Many of the resources (textbooks, workbooks, etc.) that are used do not containmany tasks that are higher level. Often, problems and examples focus on

memorization, computation, and the use of basic algorithms.

Even when students have access to high-level mathematical tasks, classroom

activities often reduce these to simple rules or algorithms for students to apply, rather

than keeping them at a high level.

There are some common misconceptions that students develop about topics at the

middle grades level, which is our primary focus (though we address other topics in

upper elementary and high school) are in ratio and proportion; functions, patterns,

and algebraic thinking; geometry and measurement; and problem solving and inquiry.Teachers often lack the training and resources to address some of these specific

topics of mathematics instruction, and the nuances related to these topics or skills.

The input students receive about mathematics from peers, family members and

others outside of the mathematics classroom is often negative, and does not support

efforts to learn mathematics at a deep conceptual level. Even when parents and

family support general mathematics learning for their children, they often focus on

low-level understanding of the mathematics and undermine the efforts of teachers to

deepen learning.

All of the materials we are developing for our resources are intended to address thesechallenges posed by research. All use research-based findings on what improves student

and teacher learning of mathematics, and they draw upon resources that have been

proven to help teachers improve the learning potential of all students.

The resources we will use draw upon a number of strategies to improve instruction and

learning, including the following:

case studies of mathematics instruction that examine the resources and teaching

practices used to support (or, in some cases, limit) student learning.

examination of student work to explore misunderstandings specific to certainmathematical topics, as well as to understand instructional moves that can address

these misconceptions.

examination of assessments and other tasks to explore how the nature of the task

can, in good examples, enhance and deepen learning, and in poor examples,

actually cause misconceptions that will stick with students for years.

Middle Start Online Mathematics Modules were developed by Middle Start and the Academy for Educational Development, in

New York, NY. This toolkit is a project of the National Forum to Accelerate Middle Grades ReformsMathematics

Improvement Toolkitand was supported by the U.S. Department of Educations Comprehensive School Reform Quality

Initiative, grant #S332B060006. Opinions expressed are those of the authors and not necessarily those of the Department.


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The slides shown in this handout

are taken from some of the Middle

Start Online materials from our initial

online workshop. They will help us

illustrate the focus and goals of the

tools.

These are followed up by a varietyof activities that might come out of

mathematics instruction in the

middle grades. These problems

and tasks are used to illustrate the

various considerations of instruction

in specific topics, as well as to bring

out potential issues in both

instructional practice and student

understanding.

Lets try the problem at right in the

space at the bottom of the page.

Please dont flip to the next page

yet. Once you respond to the poll,

move to the next page.


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How would you suggest we deal with such a problem in a class full of students?

Research suggests there are a few possible ways to address this, and it suggests how teachers

(in general) might respond to such a task for their students.

82% of U.S. Teachers would not pose the task in the first place.

99% of the remaining teachers would suggest students break the shapes into triangles, add up

the triangles, and multiply by 180.

The remainder would have students get protractors and measure various angles, add them up,and see if a pattern emerges from their results, and if so, ask students to apply the pattern to

the shapes they were given.

(Source: Third International Mathematics and Science Study)

One of the main issues we first

address is the nature of how the task

affects instruction and learning, and

how, if the task is not appropriate to

enhance student learning, little can

be done in instruction to counter this

issue.

However, even with a rigorous, rich

task that might allow for a great deal

of student learning of mathematics

concepts, this doesnt guarantee that

type of learning. Often, as research

suggests, the tasks as set up or

enacted by teachers can end up

being simplified in such a manner as

to limit student understanding as

well.

In the online and face-to-face workshop materials, we address these issues by first using this

framework to better understand the potential barriers to developing student understanding.


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We can also use a variety of

strategies that would also be

used in professional

development in a face-to-face

setting to help teachers explore

their practice.

Try this problem on your own

first, and then review the next

page to see how the various

students addressed this task.

How would you address the

understandings (or

misconceptions) that each

student has? What would this

look like in your instruction?


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webinar handout - developing student understanding in mathematics

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