video: graph! (wshs math rap song) (youtube, 4 minutes 16 seconds)
TRANSCRIPT
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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)
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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.
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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).
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What is the tan (x) ?
Submit response to PollEv.com/vyatesriley
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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
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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
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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.
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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.
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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
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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.
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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
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How We Teach Makes A Difference!
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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.
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Mathematical Practices
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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
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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.
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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.
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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.
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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?”
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Model with Mathematics
Video: Math Modelling http://youtu.be/kZc-hbQu1eY(YouTube, 4 minute 13 seconds )
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Model with Mathematics
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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.
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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.
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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.
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Attend to Precision
Video: Math Mistakes in Movies and TV
YouTubehttp://youtu.be/LXWqhazSHbc
(YouTube, 1 minute 57 seconds )
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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.
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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
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Standards for Mathematical Practices
Graphic
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Make Sense of Problems and Persevere in Solving Them
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Music Video Clip
Video: 2.71828183: The number e song http://youtu.be/ZPGHuuk2bKw(YouTube, 1 minute 52 seconds )
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Rap Video Clip
Video: Gettin' Triggy Wit It (WSHS Math Rap Song) http://youtu.be/t2uPYYLH4Zo (YouTube, 3 minutes 48 seconds )
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Conceptual Video Clip
Video: Quadratic Formulatic http://youtu.be/YCuXiujC3KE (YouTube, 3 minutes 58 seconds)
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FUNdamentals Video
The Big Bang Theory - #73http://youtu.be/TIYMmbHik08(YouTube, 1 minutes 0 seconds)
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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
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Should mathematics vocabulary be taught in the mathematics classroom?
Using your device….Submit response to PollEv.com/vyatesriley
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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
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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
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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
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Conceptual Knowledge or Procedural Knowledge?
Video: GraphingTrigFunctions.mov http://youtu.be/ccGdhpojGwU(YouTube, 4 minutes 43 seconds)
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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.
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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?
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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.
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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.
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Six-Steps for Teaching New Terms
First 3 steps – introduce and develop initial understanding.
Last 3 steps – shape and sharpen understanding.
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Provide a description, explanation, or example of new term.
Our term for today is: “obelus.”
Step 1
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Step 2
Students restate explanation of new term in own words.
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Students create a nonlinguistic representation of term.
Step 3
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Step 4
Students periodically do activities that help add to knowledge of vocabulary terms.
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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 _____.
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Step 5
Periodically students are asked to discuss terms with one another.
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“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.
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Trigonometry
SineSecant
AmplitudeAsymptote
PeriodDegreeRadian
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Step 6
Periodically students are involved in games that allow them to play with terms.
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A Vocabulary Review Activity(example: Exponential/logarithm)
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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.
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Ready to play?
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Carbon Dating
The is…
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Change-of-Base Formula
The is…
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Logarithmic Function
The is…
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Compound Interest
The is…
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Exponential Function
The is…
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base
The is…
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exponent
The is…
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one-to-one property
The is…
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quotient rule
The is…
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product rule
The is…
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power rule
The is…
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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
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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.)
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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.
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Using Humor
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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.
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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.
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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
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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.
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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.
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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.
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Contact InformationVeronica Yates-Riley
Follow me @vyatesriley on
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Thank You!
Leadership: Going on a Tangent!