What is mathematics modeling and how will it influence mathematics?

Video: Graph! (WSHS Math Rap Song) http://youtu.be/2BHzXItkByU (YouTube, 4 minutes 16 seconds)

Leadership: Going on a Tangent! Intersection & Unions, Mathematics Conference 2014

Valencia CollegeWest Campus-Mathematics DivisionOrlando, Florida

Saturday, January 4, 2014

Presenter

Veronica Yates-Riley, Ed.S.

Session Starter (mental math string)

Calculate….1. Start with the tan (π/4) .2. Divide that by the sin 30° .3. Cube this value.4. Multiply that result by cos 120° .5. Add the sin 270° .6. Multiply by cos π .7. Multiply by 5π/4 .8. Call that result “x” and find

tan(x).

What is the tan (x) ?

Submit response to PollEv.com/vyatesriley

What is the tan (x) ?

Choose the correct the answer

Type code in message line:

Text to :(type code)

-1 104598 37607

0 104607 37607

1 104637 37607

undefined 104638 37607

Session Starter (mental math string)

1. Write down the tan 45° . 12. Divide that by the sin 30° . 23. Cube this value. 84. Multiply that result by cos 120° . -45. Add the sin 270° . -56. Multiply by cos 180° . 57. Multiply by 5π/4 . 25pi/48. Call that result “x” and find tan(x).

1

Session Expectations

Session Expectation: Mathematics is taught in theory and in practice. In this session, we will discuss eight common mathematical practices; participate in various instructional games/activities: Mental Math Strings, Vocabulary games; discuss how to integrate music video clips in lessons, and discuss with colleagues best practices for instruction and assessment. B.Y.O.D.

Collegial Collaborators

Sign your name on the top of your paper.

Avoid people seated at your table.

Find a different partner for quadrants I, II, III, and IV Trade signatures. Sit down as soon as you have all signatures.

You have 2 minutes 14 seconds.

Learning GoalsThe learner will understand…The learner will understand... research-based instructional

strategies that affect student achievement in learning mathematics

characteristics of effective vocabulary instruction

Learning GoalsThe learner will be able to…

determine which strategies you will incorporate in your upper level mathematics classroom practice.

apply a six-step process for direct instruction in vocabulary.

We will learn this by doing…Discuss mathematical practicesParticipate in various instructional games/activities

Mental Math StringsPasswordVocabulary games

Discuss with colleagues best practices for instruction and assessment (e.g. humor).Reflections

How We Teach Makes A Difference!

Technological Changes

Do you remember when?

Applications were mailed to colleges.

Linked-In was a jail.

Skype was a typo.

Twitter was a sound.

4G was a parking space.

Tom Friedman. Meet the Press. September 4, 2011.

Mathematical Practices

Standards for Mathematical Practice

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

Make Sense of Problems and Persevere in Solving Them

Interpret and make meaning of the problem to find a starting point. Analyze what is given in order to explain to themselves the meaning of the problem.

Plan a solution pathway instead of jumping to a solution. Monitor their progress and change the approach if

necessary. See relationships between various representations. Relate current situations to concepts or skills previously

learned and connect mathematical ideas to one another. Continually ask themselves, “Does this make sense?”Can

understand various approaches to solutions.

Reason Abstractly And Quantitatively

Make sense of quantities and their relationships. Decontextualize (represent a situation symbolically

and manipulate the symbols) and contextualize (make meaning of the symbols in a problem) quantitative relationships.

Understand the meaning of quantities and are flexible in the use of operations and their properties.

Create a logical representation of the problem. Attends to the meaning of quantities, not just how to

compute them.

Construct Viable Arguments and Critique the Reasoning of Others

Analyze problems and use stated mathematical assumptions, definitions, and established results in constructing arguments.

Justify conclusions with mathematical ideas. Listen to the arguments of others and ask useful

questions to determine if an argument makes sense. Ask clarifying questions or suggest ideas to

improve/revise the argument. Compare two arguments and determine correct or

flawed logic.

Model with Mathematics• Understand this is a way to reason quantitatively and abstractly

(able to decontextualize and contextualize).

• Apply the mathematics they know to solve everyday problems.

• Are able to simplify a complex problem and identify importantquantities to look at relationships.

• Represent mathematics to describe a situation either with anequation or a diagram and interpret the results of a mathematical situation.

• Reflect on whether the results make sense, possibly improving/revising the model.

• Ask themselves, “How can I represent this mathematically?”

Model with Mathematics

Video: Math Modelling http://youtu.be/kZc-hbQu1eY(YouTube, 4 minute 13 seconds )

Model with Mathematics

Use Appropriate Tools Strategically

Use available tools recognizing the strengths and limitations of each.

Use estimation and other mathematical knowledge to detect possible errors.

Identify relevant external mathematical resources to pose and solve problems.

Use technological tools to deepen their understanding of mathematics.

Use Appropriate Tools Strategically

pencil and paper concrete models (e.g. Algebra tiles, tangrams) ruler protractor calculator spreadsheet graph paper computer algebra system statistical package, or dynamic geometry

software Graphing utilities etc.

Attend to PrecisionCommunicate precisely with others and

try to use clear mathematical language when discussing their reasoning.

Understand the meanings of symbols used in mathematics and can label quantities appropriately.

Express numerical answers with a degree of precision appropriate for the problem context.

Calculate efficiently and accurately.

Attend to Precision

Video: Math Mistakes in Movies and TV

YouTubehttp://youtu.be/LXWqhazSHbc

(YouTube, 1 minute 57 seconds )

Look for and Make Use of Structure

Apply general mathematical rules to specific situations.

Look for the overall structure and patterns in mathematics.

See complicated things as single objects or as being composed of several objects.

Look for and Express Regularity in Repeated Reasoning

See repeated calculations and look for generalizations and shortcuts.

See the overall process of the problem and still attend to the details.

Understand the broader application of patterns and see the structure in similar situations.

Continually evaluate the reasonableness of their intermediate results

Standards for Mathematical Practices

Graphic

Make Sense of Problems and Persevere in Solving Them

Music Video Clip

Video: 2.71828183: The number e song http://youtu.be/ZPGHuuk2bKw(YouTube, 1 minute 52 seconds )

Rap Video Clip

Video: Gettin' Triggy Wit It (WSHS Math Rap Song) http://youtu.be/t2uPYYLH4Zo (YouTube, 3 minutes 48 seconds )

Conceptual Video Clip

Video: Quadratic Formulatic http://youtu.be/YCuXiujC3KE (YouTube, 3 minutes 58 seconds)

FUNdamentals Video

The Big Bang Theory - #73http://youtu.be/TIYMmbHik08(YouTube, 1 minutes 0 seconds)

Rigor and Relevance

“If a [student] sees something they relate to, they’ll become personally engaged in the learning process and that will enable them to obtain rigor. A statement has been made that we confuse obedient students with motivated students. There are a group of [students] who will do well simply because they’re obedient. But for the [students] who are hardest to reach, you’ve got to motivate them because they won’t do it simply because they’re obedient. The thing is changing how you teach.”

-Willard Daggett, CEO for the International Center for Leadership in Education

Should mathematics vocabulary be taught in the mathematics classroom?

Using your device….Submit response to PollEv.com/vyatesriley

Should mathematics vocabulary be taught in the mathematics classroom?

Before you answer…1. Access your cell phone2. Prepare to send a text message3. In the “To” line type: 376074. In the message section type: 104702

then type your response5. Send your text message6. Look at the screen in the front of the

classroom to see others responses7. You may respond at PollEV.com if you

don’t want to use your cell phone

Should mathematics vocabulary be taught in the mathematics classroom?Type your response Type code in

message line:Text to :(type code)

(free response) 104702 37607

Declarative Knowledge (Information and Ideas)

-Vocabulary-Details-Organizing Ideas-Will understand…..-nouns

Procedural Knowledge (Skills and Processes)

-Skills and Tactics-Processes-Will be able to….-verbs

Categories of Subject Matter Knowledge

Conceptual Knowledge or Procedural Knowledge?

Video: GraphingTrigFunctions.mov http://youtu.be/ccGdhpojGwU(YouTube, 4 minutes 43 seconds)

Teaching Mathematics Vocabulary

1) The teacher explains a new word — going beyond reciting its definition.

2) Students restate or explain the new word in their own words.

3) Students create a nonlinguistic representation of the word.

4) Students engage in activities to deepen their knowledge of the new word.

5) Students discuss the new word.6) Students play games to review new

vocabulary.

Why Vocabulary Instruction?

Why does vocabulary instruction have such a profound effect on student comprehension of academic content?

What do these words have in common: complex number, completing the square, square root, vertex, axis of symmetry, minimum, maximum, end behavior, translations, intercepts, solutions, zero

When would knowing this vocabulary be helpful to you?

Impact of Direct Vocabulary Instruction

Research shows a student in the 50th percentile in terms of ability to comprehend the subject matter taught in school, with no direct vocabulary instruction, scores in the 50th percentile ranking.

The same student, after specific content-area terms have been taught in a specific way, raises his/her comprehension ability to the 83rd percentile.

What It Means to Us…

It is not necessary for all vocabulary terms to be directly taught.

Yet, direct instruction of vocabulary has been proven to make an impact.

Six-Steps for Teaching New Terms

First 3 steps – introduce and develop initial understanding.

Last 3 steps – shape and sharpen understanding.

Provide a description, explanation, or example of new term.

Our term for today is: “obelus.”

Step 1

Step 2

Students restate explanation of new term in own words.

Students create a nonlinguistic representation of term.

Step 3

Step 4

Students periodically do activities that help add to knowledge of vocabulary terms.

Review Activity (step 4) Solving Analogy Problems

One or two terms are missing. Please think about statements below, turn to your elbow partner and provide terms that will complete following analogies.

three is to one-third as sine is to ______.

ax2+bx+c is to zero as _____ is to _____.

Step 5

Periodically students are asked to discuss terms with one another.

“Talk a Mile a Minute” Activity (Step 5)

Teams of 3-4 Designate a “talker” for each round. Try to get team to say each word by

quickly describing them. May not use words in category title

or rhyming words.

Trigonometry

SineSecant

AmplitudeAsymptote

PeriodDegreeRadian

Step 6

Periodically students are involved in games that allow them to play with terms.

A Vocabulary Review Activity(example: Exponential/logarithm)

Playing PASSWORD Games

PASSWORD Directions: Type a vocabulary word on each of the following 10 slides in the subtitle textbox. When complete, run the show by pressing F5 on the keyboard.

One student stands with back to this presentation.

The class gives the student clues to the vocabulary word onscreen as a clock keeps time.

The student tries to guess the word before the buzzer.

Ready to play?

Carbon Dating

The is…

Change-of-Base Formula

The is…

Logarithmic Function

The is…

Compound Interest

The is…

Exponential Function

The is…

base

The is…

exponent

The is…

one-to-one property

The is…

quotient rule

The is…

product rule

The is…

power rule

The is…

Vocabulary CharadesGame Activity

Please stand. Using your arms, legs, and bodies,

show the meaning of each term below: Identity Function Quadratic Function Cubic Function Reciprocal Function Logarithmic Function

Card Sort: Pairing

This involves students pairing cards together looking for some attribute or relationship the most common (and closed) of these being pairing a problem and a solution, but it could be a shape and name/property etc.

When designing cards for matching into pairs, it is not a bad idea to put in some cards that do not have a matched pair in the set particularly if this highlights a misconception ( f-1(x) = 1/f(x) etc.)

Card Sort: Grouping

This involves grouping cards together for instance; For which problems on the cards would you use the sine ratio?

Which problems are to do with the ratio 2:1? Sort the angles into right angles, acute, obtuse

and reflex Group together the algebraic expressions

according to their number of terms Sort vocabulary terms by units/lessons* Note Venn diagrams may be useful here for

cards that fit into more than one group or do not belong to any.

Using Humor

Implementing Mental Math Strings

1) Determine extended math facts you want your students to know.

2) Build your mental math strings. 3) Do one string each day4) Preview information in the mental math

string. 5) Implement the mental math string. 6) Share results, congratulate students who

succeed and encourage those who don’t.7) Invite a student who succeeds to repeat the

string in front of the class.8) Invite students to make their own and share

with the class.

Implementing Mental Math Strings (example)

1. Consider y = 6x + 12.2. Start with the y-intercept.3. Add the slope of the line.4. Divide that by the x-intercept.5. Add the value of y when x = ½ .6. Add the value of x when y is 6.7. Multiply that by the square of

the zero of the function.

Implementing Mental Math Strings

Consider y = 6x + 12Start with the y-intercept. 12Add the slope of the line. 12 + 6 =

18Divide that by the x-intercept.

18/-2 = -9

Add the value of y when x = ½ .

-9 +15 = 6

Add the value of x when y is 6.

6 + -1 = 5

Multiply that by the square of the zero of the function.

(5)( 4) = 20

Keeping Track of Student Progress Learning Vocabulary

Level 4:

I understand even more about the term than when I was taught.

Level 3: I understand the term and I’m not confused about any part of what it means.

Level 2: I’m a little uncertain about what the term means, but I have a general idea.

Level 1: I’m very uncertain about the term. I really don’t understand what it means.

Vocabulary Management

5, 6, 7 terms per week for 30 weeks to teach target terms.

Set aside time periodically to engage students in vocabulary activities, adding to knowledge base.

Allow students to discuss terms. Encourage students to add

information to notebooks.

Reflections (Exit Slip)

One thing that you loved

learning about today

One all encompassing statement that

summarizes today’s session.

3 most

important facts from

today’s session.

Four things that are important concepts from

today’s session – one in each

corner.

Contact InformationVeronica Yates-Riley

vyatesriley@valenciacollege.edu

Follow me @vyatesriley on

Thank You!

Leadership: Going on a Tangent!