Elementary ACT meeting

Mathematics DepartmentSeptember 26, 2013

Mathematical literacy

Warm up

Please justify that25 / 5 = 14

Justifying work

“revision is where the real mathematics happens”

•Dr. Ravi Vakil, 2012

Warm up response

Clear Learner Objectives

• Gain an understanding of why mathematical writing is critical.

• Tools for incorporating mathematical writing in class

Why write in math class?

Research says…

In the Texas Essential Knowledge and Skills

A(2) “…. in Kindergarten-Grade 2, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language into mathematical language and symbols. Students use objects to create and identify patterns and use those patterns to express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. Students progress from informal to formal language to describe two- and three-dimensional geometric figures and likenesses in the physical world. Students begin to develop measurement concepts as they identify and compare attributes of objects and situations. Students collect, organize, and display data and use information from graphs to answer questions, make summary statements, and make informal predictions based on their experiences ”

(K-2, Texas Education Agency, 2012)

In the Texas Essential Knowledge and Skills

• A(2) “…. in Grades 3-5, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use algorithms for addition, subtraction, multiplication, and division as generalizations connected to concrete experiences; and they concretely develop basic concepts of fractions and decimals. Students use appropriate language and organizational structures such as tables and charts to represent and communicate relationships, make predictions, and solve problems. Students select and use formal language to describe their reasoning as they identify, compare, and classify two- or three-dimensional geometric figures; and they use numbers, standard units, and measurement tools to describe and compare objects, make estimates, and solve application problems. Students organize data, choose an appropriate method to display the data, and interpret the data to make decisions and predictions and solve problems.

• (3-5, Texas Education Agency, 2012)

It’s in the College and Career Readiness Standards

(Texas College and Career Readiness Standards, 2009)

It’s part of Mathematics

“it centers on proof, argumentation, and perspective, convincing people, making them understand it is central to mathematics…..as a result it’s probably the only subject where elegance in the writing is essential to how we see the subject”

- Dr. Ravi Vakil, 2012

It matters to mathematicians

It supports the development of Academic Language

Knowing where the they stand within the content is important, but learning how they acquired the knowledge is relevant to continuing comprehension

(D’Ambrosio, 1997)

• “There is no one-to-one correspondence between the words and symbols they represent.”

• “Mathematics text are conceptually packed, have high density.”

• “Require left-to-right as well as up-and-down eye movement.”

• “Use numerous symbolic devices such as charts and graphs.”

(Wright, 2008)

It enriches teaching practice

• Identify student misconception.

• Improve delivery of instructions

• Deepen classroom questioning

Quick GlanceWriting is essential in mathematics as it:

• Increases and deepens content understanding• Helps Identify misconceptions• Improves lesson planning and delivery of instruction

“Writing is nature’s way of letting us see how sloppy our thinking is” (Wolfe, 2001)

What should math writing look like?

Types of writing

Opinion: Support a choice. The writer must use evidence to clearly argue his/her opinion.

Content: Provide descriptive information about a topic.

K-2 The student uses mathematical (oral) language to express understanding by using words, sentence stems, and full sentences to express and label mathematical content. (progress)

3-5 The writer must use vivid details to paint a picture for the reader.

Process: Explain the steps or procedures of something.K-2 The student translates informal language to mathematical

language and symbols. By developing summary statements. 3-5 The writer must provide a clear coherent explanation of

problem solving and procedure

(Burns 2004, Russek 1998, Schmidt 1985)

Example 1a:Mathematics Content Writing

Example 1b:Mathematics Content Writing

Example 2a:Mathematics Process Writing

Example 2b:Mathematics Process Writing

ExemplarsWord problems that focus on specific math content

Betty loves blocks. First she made a tower 2 blocks high. Next to it she made a tower 4 blocks high. Next to those she made a tower 6 blocks high. If she continues this pattern, how many blocks in all will she have used after she has completed a tower 10 blocks high?

Elementary School Level Exemplar

K-2

Betty’s Blocks

Student “A” response

Betty’s Blocks

Betty’s BlocksStudent “B” response

To the DetailElementary School Level Exemplar

3-5

Mike was born on February 20, 1988, at 11:05 a.m. His birthday falls on a Friday this year, but he will be celebrating it with a party on Saturday, February 21, 1998, at 3:00 p.m.

On the birthday cake she made, his mom wants to write the exact age he will be at the start of his party. How could she write it?

To the DetailStudent “A” response

To the DetailStudent “B” response

Make sure your Math writing includes:

“elegance in the writing is essential to how we see the subject” Dr. Vakil

Writing Practice time

Most Importantly…

Providing descriptive feedback allows students to learn and understand their mistakes, it also

influences and molds the way a teacher conducts instruction.

(Barry, 2008)

Some Feedback methods

Type of feedback

FEEDBACK Practice timE

Mathematical Writing FrequencyDaily Writing Weekly Writing 9 Week Project

2 – 3 sentences At least a paragraph About 1 -2 pages

• Quick write• Exit tickets• Foldable• Open ended question• Note-taking*• Parking lot• Tweet• Quick check• Journal writing

• Writing letters• Summaries• Comic strip• Vocabulary• Big book story

Interactive math story World scape literature

• Research project• Steward Murphy Math

start literature series• Math-Cliffs• Exemplars

* Provide students opportunities to use their notes during a test to encourage good note taking.

Please Remember that…

“Teachers incorporate writing in math class to help students reflect on their learning, deepen their understanding of important concepts by explaining and providing examples of those concepts, and make important connections to real-life applications of the math they are learning.”

(Mathwire.com, 2013)

Final Thought

“Every year, we buy ten cases of paper at $35 each; and every year we sell them for about $1 million each. Writing… well… is very important to us”

Bill Browing, President of Applied Mathematics, Inc.