Developing a Cross-Disciplinary STEM Based High School CurriculumTALITHA M. WASHINGTONASSOCIATE PROFESSOR OF MATHEMATICS

HOWARD UNIVERSITY

AUGUST 21, 2014

JOHN HARKLESSASSOCIATE PROFESSOR OF CHEMISTRY

HOWARD UNIVERSITY

Washington Math and Science Public Charter School’s Mission

To provide a rigorous education that integrates mathematics and science instruction with technology resulting in highly self-motivated students.

http://wmstpchs.org/

NSF Report – 2013 Women, Minorities, and persons with Disabilities in Science and Engineering

Number of STEM jobs has increased by 30% since 2000

http://www.nsf.gov/statistics/wmpd/2013/digest/

Three Stages of Racism Dr. Richard Tapia, Rice University

1. Denied access2. Implementation of separate but equal programs3. Lower expectations for minorities, efficient

understanding, and misguided corrections

http://www.caam.rice.edu/~rat/

Stereotype Threat

A person’s ability is suppressed by anxiety about confirming a negative stereotypeAffects performance by increasing negative thoughts, physical arousal, working memory capacity, performance expectations, or increase or reduce effortPrevention: Teach students effects of “stereotype threat” (it can actually reduce anxiety and improve test performance) and provide stereotype-busing information

http://www.laurelschool.org/about/Research2.cfm

STEM Across the Curriculum

Rubric of Selected Module

Include concepts and methods from two or more disciplinary traditionsBalance of disciplinary perspectives and approaches to advance student learning and understandingConvey ways which the integration of disciplinary views advance understandingDevelop an awareness of the limitations and benefits of the contributing disciplines

Task: Develop a Module in Teams

Prezi.com

Storytelling tool for presenting ideas on a virtual canvas Cloud-based presentation software Used by teachers and students to collaborate on presentations with multiple users having access and the ability to edit the same presentation Allow students to construct and present their knowledge in different learning styles

http://en.wikipedia.org/wiki/Prezi

Report: Share Modules

Goal: Infuse STEM Across the Curriculum

Science Project

http://www.sciencebuddies.org/science-fair-projects/project_display_board.shtml

Scientific Method

1. Choose a problem to investigate or a project to carry out2. Do background research to learn as much as possible about the topic you

are working on3. Form a hypothesis (educated guess) about your results and/or a plan to

carry out your project4. Conduct experiments to test your hypothesis or carry out your project

plan5. Analyze your data (results) – this should include determining any

limitations or problems in your data or experimental methods6. Discuss your results and state your conclusions (these must be supported

by your data)

http://www.sciencemontgomery.org/students/

Project Components

Poster

ProposalRe-search

Papers

Oral Presentations

Re-searchContribute novel perspectives and

ideas

Create knowledge

Gain deep understanding

Project: A Cross-Disciplinary Approach

Historical relevance Writing of the paperSocietal impactCultural connectionPolitical impactsArtistic aesthetic

http://writing.colostate.edu/guides/guide.cfm?guideid=83

Task: Develop a Step-by-Step Guide for an Ideal Cross-Disciplinary Project

Rubric of the Project

Articulate how teachers from multiple disciples will lead and evaluate the projectProvide checkpoints that indicate work that must be completed that would lead to the final projectInclude concepts and methods from two or more disciplinary traditions the project must satisfySpecify and describe the cross-disciplinary components of the project and how they enhance student learning

Report: Share Project Guides

Goal: Cross-Disciplinary Project

Continue the STEM Cultivation

It is important to have students develop a sense of ownership about what they are doing…Science is very challenging, collective work. No matter how hard you work, the importance is to make collective advancements over time. I love impacting young people, encouraging them to get their Ph.D.'s while working on questions that matter to them and their communities. They are the engines of improvement in our society. There’s nothing like having the job that I have.

Dr. Carlos Castillo-Chávez, Arizona State University

http://en.wikipedia.org/wiki/Carlos_Castillo-Chavez

S. Maloy 10/01

Guidelines for Writing a Scientific Paper

Writing an effective scientific paper is not easy. A good rule of thumb is to write as if your paperwill be read by a person who knows about the field in general but does not already know whatyou did. Before you write a scientific paper read some scientific papers that have been written inthe format of the paper you plan to use. In addition to the science, pay attention to the writingstyle and format.

Abstract: An abstract is a succinct (one paragraph) summary of the entire paper. The abstractshould briefly describe the question posed in the paper, the methods used to answer this questionthe results obtained, and the conclusions. It should be possible to determine the major points of apaper by reading the abstract. Although it is located at the beginning of the paper, it is easiest towrite the abstract after the paper is completed.Introduction: The Introduction should (i) describe the question tested by the experimentsdescribed in the paper, (ii) explain why this is an interesting or important question, (iii) describethe approach used in sufficient detail that a reader who is not familiar with the technique willunderstand what was done and why, and (iv) very briefly mention the conclusion of the paper.Materials and Methods: The Materials and Methods section should succinctly describe whatwas actually done. It should include description of the techniques used so someone could figureout what experiments were actually done. The details of a published protocol do not need to bereproduced in the text but an appropriate reference should be cited – e.g., simply indicate “weredone as described by Hughes et al. (4)”. Any changes from the published protocol should bedescribed. It is not appropriate to indicate volumes of solutions added – instead indicate therelevant information about the experiment such as final concentrations used, etc.Results: Begin each paragraph with an opening sentence that tells the reader what question isbeing tested in the experiments described in that paragraph. Write the opening sentence in boldfont for emphasis. (Sometimes a complete sentence is used and sometimes a short phrase is used– either style is OK but the style should be used consistently throughout the manuscript.) Anyresults that include multiple data points that are critical for the reader to evaluate the experimentshould be shown in tables or figures. However, the results should be summarized inaccompanying text. When referring to a particular table or figure, they should be capitalized(e.g., Table 1, Figure 6, etc.) The text of the Results section should be succinct but shouldprovide the reader with a summary of the results of each table or figure.Not all results deserve a separate table or figure. As a rule of thumb, if there are only a fewnumerical results or a simple conclusion describe the results in the text instead of in a table orfigure.Your paper should focus on what worked, not things that did not work (unless they didn’t workfor reasons that are interesting and provide biological insights).Tables and Figures: All tables and figures should be put into a contextual framework in thecorresponding text. A table of strains used should be mentioned in the Materials and Methodssection, a table of results should be summarized in the Results section, a figure showing abiosynthetic pathway should be described in the Discussion section, etc. Tables and figuresshould present information in a format that is easily evaluated by the reader. A good rule of

http://www.sci.sdsu.edu/~smaloy/MicrobialGenetics/topics/scientific-writing.pdf

S. Maloy 10/01

thumb is that it should be possible to figure out the meaning of a Table or Figure withoutreferring to the text. Tables and figures should typically summarize results, not present largeamounts of raw data. When possible, the results should provide some way of evaluating thereproducibility or statistical significance of any numbers presented.Tables should be sequentially numbered. Each table should have a title (shown above the table)that describes the point of the table. For example, “Table 1. Bacterial strains and plasmids usedin this study.” If necessary to interpret the table, specific descriptions about what a resultrepresents or how the results were obtained can be described in a legend below the table.Figures should be sequentially numbered. Each figure should have a title (shown below thetable) that describes the point of the table. For example, “Figure 1. Isolation of MudJ insertionmutants.” If necessary to interpret the figure, specific descriptions about what a result representsor how the results were obtained can be described immediately following the title.Tables and figures may be printed on separate pages that follow the Reference section.Alternatively, the tables and figures may be integrated into the paper if you are using a pagelayout program. However, if they are integrated into the paper make sure that there is not a pagebreak in the middle of a table or figure. Do not wrap text around the outside of tables and figures– if the results are important enough to show as a table or figure they should stand out on thepage, not be buried in text.Discussion: Do not simply restate the results — explain your conclusions and interpretations ofthe Results section. How did your results compare with the expected results? What furtherpredictions can be gleaned from the results?Citations: It is essential to credit published papers for work mentioned in your manuscript.There are a variety of ways of citing references in the text – the style used depends upon thepolicy of the journal. In text citations should refer to reference list. Do not rewrite title ofreferences in text.Reference lists: Like citations, a variety of reference formats are used by different journals. Foran example of a commonly used example, see “Instructions to authors” on ASM web site(http://jb.asm.org/misc/ifora.shtml) or examples from published manuscripts.Genetic nomenclature: Use correct genetic nomenclature for both genotype and phenotype. Toreview the rules for bacterial genetic nomenclature, see the Microbial Genetics topics link.Format: Certain general rules are commonly followed in scientific writing.Flow. Readers interpret prose more easily when it flows smoothly, from background to rationaleto conclusion. Don’t force the reader to figure out your logic – clearly state the rational. Inaddition, it is much easier on the reader if you explicitly state the logic behind any transitionsfrom one idea to another.Abbreviations. Use standard abbreviations (hr, min, sec, etc) instead of writing complete words.Some common abbreviations that do not require definition are shown on the attached table.Define all other abbreviations the first time they are used, then subsequently use the abbreviation[e.g. Ampicillin resistant (AmpR)]. As a general rule, do not use an abbreviation unless a term isused at least three times in the manuscript. With two exceptions (the degree symbol and percentsymbol), a space should be left between numbers and the accompanying unit. In general,abbreviations should not be written in the plural form (e.g. 1 ml or 5 ml, not mls).

S. Maloy 10/01

Past, present, and future tense. Results described in your paper should be described in past tense(you’ve done these experiments, but your results are not yet accepted “facts”). Results frompublished papers should be described in the present tense (based upon the assumption thatpublished results are “facts”). Only experiments that you plan to do in the future should bedescribed in the future tense.Third vs first person. It is OK to use first person in scientific writing, but it should be usedsparingly – reserve the use of first person for things that you want to emphasize that “you”uniquely did (i.e. not things that many others have done as well). Most text should be written inthe third person to avoid sounding like an autobiographical account penned by a narcissisticauthor. However, it is better to say “It is possible to ..” than to say “One could ...”. Writing thatuses the impersonal pronoun “one” often seems noncommittal and dry.In addition, inanimate objects (like genes, proteins, etc) should be described in third person, notwith anthropomorphic or possessive terms (e.g., instead of saying “its att site”, say “thechromosomal att site”).Empty phrases. Avoid using phrases that do not contribute to understanding. For example, thefollowing phrases could be shortened (or completely deleted) without altering the meaning of asentence: “the fact that ...” (delete); “In order to ...” (shorten to simply “To ...”). Likewise, thetitle of a table of results does not benefit from the preface “Results of ...”. In short, don’t usemore words than you need to make your point.Specify. If several expressions modify the same word, they should be arranged so that it isexplicit which word they modify. It is common to use a pronoun such as “it” or “they” to refer toa concept from the previous sentence. This is OK as long as there is only one concept that “it” or“they” means. However, if there are more than one concepts it is easy for the reader to getconfused about what the pronoun is meant to specify (even if you know which one you mean). Itis better to error on the side of redundancy by repeating the concept in subsequent sentences,than to take the chance of confusing the reader. Don’t make the reader guess what you mean.Parentheses. Avoid double parentheses. For example, “Three gene products catalyze reactions inthe pathway for proline biosynthesis (Figure 1) (3)” could be reworded to say “Figure 1 showsthe three reactions of the pathway for proline biosynthesis (3).”Proofreading: Always spellcheck your paper and carefully proofread your paper beforesubmission. In addition to checking for errors and typos, read your paper to yourself as if youwere reading it out loud to ensure that the wording and sentence construction is not clumsy.

SOME USEFUL RESOURCES:

Instructions to Authors, J. Bacteriol.[http://jb.asm.org/misc/ifora.shtml]Word usage in scientific writing [http://www.ag.iastate.edu/aginfo/checklist.html]Dangling modifiers [http://owl.english.purdue.edu/handouts/grammar/g_dangmod.html]

S. Maloy 10/01

Alley, M. 1996. The craft of scientific writing, 3rd edition. Prentice Hall, NJ. [and accompanyingweb site: http://filebox.vt.edu/eng/mech/writing/]

Day, R. 1998. How to write and publish a scientific paper, 5th edition. Orynx Press.Day, R. 1995. Scientific English: A guide for scientists and other professionals, 2nd edition.

Orynx Press.Goben, G., and J. Swan. 1990. The science of scientific writing. Am. Scientist 78: 550-558.

[Available online at http://www.research.att.com/~andreas/sci.html]McMillan, V. 1988. Writing papers in the biological sciences. Bedford Books, NY.Strunk, W., and E. B. White. 1979. The elements of style, 3rd edition. MacMillian Publishing Co.

S. Maloy 10/01

Some standard abbreviations:

Unit Abbreviation Defination

Time sec Secondsmin Minuteshr Hours

Weight g Gramsmg Milligrams (10-3 g)µg Micrograms (10-6 g)

Volume l Literml Milliliter (10-3 l)µl Microliter (10-6 l)

Nucleotide length bp Base pairsKb Kilobase pairs (103 bp)Mb Megabase pairs (106 bp)

Common molecular biology terms A, T, G, C, U Adenine, Thymidine, Guanine,Cytosine, Uracil

DNA Deoxyribonucleic acidRNA Ribonucleic acidNTP Nucleotide triphosphatedNTP Deoxyribonucleotide triphosphateNAD Nicotinamine adenine dinucleotideEDTA Ethylenediamine tetraacetic acidEGTA Ethylene glycol-bis(b-aminoether)

N,N,N',N'-tetra acetic acidTRIS Tris(hydroxyamino)methaneUV Ultraviolet lightPFU Plaque forming units

Symbols for chemical elements C, N, P, etc Carbon, nitrogen, phosphorus, etcOne- or three-letter abbreviationsfor amino acids

e.g. Ala (A) Alanine

Arg (R) Arginine

S. Maloy 10/01

Asn (N) AsparagineAsp (D) Aspartic acidCys (C) CysteineGln (Q) GlutamineGlu (E) Glutamic acidGly (G) GlycineHis (H) HistidineIle (I0 IsoleucineLeu (L0 LeucineLys (K) LysineMet (M) MethioninePhe (F) PhenylalaninePro (P) ProlineSer (S) SerineThr (T) ThreonineTrp (W) TryptophanTyr (Y) TyrosineVal (V) Valine

Methuen High School Science Fair Judging Rubric

Student’s Name:

Project #:

Project Category: Judge #:

Project Title: Grade:

Supe

rior

Abo

ve A

vera

ge

Ave

rage

Bel

ow A

vera

ge

No

Evid

ence

Scientific Method 1. Clear and specific question 4 3 2 1 0 2. Clear and specific hypothesis identifying independent and dependent variables

4 3 2 1 0

3. Developed good procedures for testing the hypothesis, including use of control variables

4 3 2 1 0

4. Clear and thorough processes for data observation and collection 4 3 2 1 0 5. Ran sufficient trials (at least 3) 4 3 2 1 0 6. Accurate experimental techniques 4 3 2 1 0 7. Complete and thorough data (logs, graphs, tables, photos etc) 4 3 2 1 0 8. Derived conclusions from appropriately organized and summarized data 4 3 2 1 0 9. Related conclusions back to the hypothesis 4 3 2 1 0 Opportunities for Improvement:

Scientific Knowledge 10. Accessed a minimum of three age-appropriate sources for background research

4 3 2 1 0

11. Clearly identified and explained key scientific concepts relating to the experiment

4 3 2 1 0

12. Used scientific principles and/or mathematical formulas correctly in the experiment

4 3 2 1 0

13. Student suggest changes to the experimental procedure and/or possibilities for further study while evaluating the success and effectiveness of the project.

4 3 2 1 0

Opportunities for Improvement:

Presentation 14. Neat, well organized, and visually appealing 4 3 2 1 0 15. Included key components to provide a thorough piece of the project (title, abstract, variables, hypothesis, summary of research findings, materials and procedures, data charts, graphs and/or pictures, results and conclusion)

4 3 2 1 0

16. Pictures and diagrams effectively convey information about the science fair project

4 3 2 1 0

17. Included a complete and detailed lab notebook 4 3 2 1 0 18. Presenter is able to answer questions related to the project 4 3 2 1 0 19. Student presents relevance of the project 4 3 2 1 0 Opportunities for Improvement:

Simplicity 20. Appropriate Materials and Construction 4 3 2 1 0 21. Clarity of overall project 4 3 2 1 0 22. Original topic or approach 4 3 2 1 0 23. Demonstrates knowledge of the scientific method 4 3 2 1 0 24. Written document clearly demonstrates use of research, experimentation and analysis skills

4 3 2 1 0

25. Shows enthusiasm and interest in the project 4 3 2 1 0 Opportunities for Improvement:

TOTAL SCORE: ______/100

Media Literacy Unit Plan Seventh Grade

25

Week Two, Lesson #8: Body Image

Objectives: • Students will identify and explain the individual’s responsibility to

…peers, the community, including the need for civility, respect fordiversity and the rights of others (10.54.6021).

• Students will analyze the media’s influence on government, social andcultural norms….(10.54.3843).

• Students will analyze point of view and embedded values in mediamessages (10.54.3842).

• Students will thoroughly evaluate the influences of media and culture onhealth (10.54.7091).

Materials: Definition of Body Image worksheet, Growth Chart overheads, overhead projector, What is ‘normal’ poster

Body Image Content Rationale: Students will recognize that the media’s portrayals of body are narrow, unrealistic and unhealthy. Students will question media depictions of the body, using deconstruction techniques. Students will reflect on their developing understanding of a healthy body image and will be presented with healthy images of the body. Students will develop an appreciation for different societies’ definitions of beauty.

Instructional Procedure: 1. Students will make their presentations of marketing projects. This should take up about

half of the class period. [Transition to Body Image]

2. Discuss what is ‘stereotypical’ and compare that to what is ‘typical’, then moving on towhat is ‘normal’. ‘Normal’ and ‘Average’ are not necessarily the same concept. Make sure students understand the subtle differences between all these vocabulary words.

3. What is normal vs. what is represented as normal?i. Body Image: handout definition of body image worksheet.

ii. Growth charts: Show the transparencies briefly to demonstrate the range ofhealthy bodies. Note: this isn’t a chance for students to see where each person ison the chart, just a visual image to point out the large range of ‘normal’.

iii. Show the poster of what is normal, also noting the variety in body types.4. Discussion: How do we measure ourselves? Bathroom scale? We will examine the

power of media in how we think about how the world sees us and how we see ourselves.

Stats/Facts/Resources:

• Two out of five women and one out of five men would trade three to five years of theirlife to achieve their weight goals.

• In 1970 the average age of a girl who started dieting was 14; by 1990 the average dietingage fell to 8.

Standards Met:

Lesson meets: Media Literacy

Standard: 10.54.3840

Social Studies Standard:

10.54.6020

Health Enhancement

Standard: 10.54.7070

http://www.youthconnectionscoalition.org/pdfs/MS7LessonPlans.pdf

Media Literacy Unit Plan Seventh Grade

26

• A study found that women overestimate the size of their hips by 16% and their waists by 25%, yet the same women were able to correctly estimate the width of a box.

• After viewing images of female fashion models, seven out of ten women felt more depressed and angry than prior to viewing the images.

• The “ideal” woman - portrayed by models, Miss America, Barbie dolls, and screen actresses - is 5’5, weighs 100 pounds and wears a size 5.

• Young girls are more afraid of becoming fat than they are of nuclear war, cancer, or losing their parents.

• One out of three women and one out of four men are on a diet at any given time. Two thirds of dieters regain the weight within one year and virtually all regain it within five years.

• 35% of occasional dieters progress into pathological dieting. • The diet industry (diet foods, diet programs, diet drugs, etc.) takes in over $40 billion

each year and continues to grow. • 30% of women chose an ideal body shape that is 20% underweight and an additional

44% chose an ideal body shape that is 10% underweight. • The average U.S. woman is 5’4” and weighs 140 pounds whereas the average U.S. model

is 5’11” and weighs 117 pounds. --From the University of Colorado webpage on Body Image: http://www.colorado.edu/StudentGroups/wellness/NewSite/BdyImgShockingStats.html • For more CDC information on growth charts, see their webpage at: http://www.cdc.gov/nchs/about/major/nhanes/growthcharts/clinical_charts.htm#Clin%202

www.jaguarstones.comDIGGING DEEPER: MAYA MATH 1

Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

Essential Question: Was math discovered or invented?

Sub questions: - How have different cultures have created systems to represent the patterns or relationships of mathematics?

- How does learning Mayan math deepen our understanding of the Arabic system that we use?

Standards: - Develop meaning for integers and represent and compare quantities with them.

- Compare and contrast the properties of numbers and number systems.

Materials: - Video modeling Mayan math instruction (provided)

- Toothpicks, beans and shells, or other markers

- Math grid and practice worksheets (provided)

- Access to research materials

Objectives: TSW: - Demonstrate a working knowledge and understanding of Maya numerals and

arithmetic.

- Explain the role of zero in addition, subtraction and multiplication.

- Compare and contrast Maya mathematical concepts with those of other cultures (eg Roman numerals), and discuss the relative strengths and weaknesses of each.

UNIT: MAYA MATHSUBJECT: MATHEMATICSGRADE: 5–9

“There’s not much point in making wheeled carts if you don’t have draft animals to pull them,” sniffed Lola. “Besides we were busy inventing the Maya calendar (and) the concept of zero . . .”

The Jaguar Stones, Book One: Middleworld, EgmontUSA, ISBN 978-1-60684-071-9, page 209

Note to teachers: The most effective way for kids to experience and understand the 20-based Maya number system is to physically manipulate toothpicks, beans and shells or other markers.

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Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

DIGGING DEEPER: MAYA CIVILIZATION 2

Rationale: The Maya were advanced mathematicians, and one of the first societies to successfully incorporate the concept of zero into their calculations. Unlike our own culture, which bases its numbering system on the numeral ten (likely because of the ten fingers on human hands), the Maya developed a system based upon the number 20 (fingers and toes). Numerals were represented by a series of dots (1 dot = 1) and bars (1 bar = 5) stacked vertically on top of one another. When the number reached twenty, a dot was moved into a second place value (analogous to our “tens” position), situated directly above the original number. Zero was represented most often by a shell.

Key Vocabulary: - Decimal System: method of counting based on the number 10.

- Vigesimal System: method of counting based on the number 20.

ACTIVITY 1 THE MAYA NUMBER SYSTEM

NOTE: Before the lesson, prepare the materials and watch the modeled instruction.

Lead/Inquiry: Was math discovered or invented? Using journaling, Pair/Share or a KWL chart lead the class through a discussion of the

development of math and how/why it evolved. Review the term decimal system and how it might have been created.

Procedure: Pass out the Maya Numerals Worksheet to the class. Give the students five minutes as archeologists to decipher the Maya numerals as best as they can using the incomplete key provided. Have students share ideas about how the system works, but do not confirm guesses.

Model adding a two-digit number silently using toothpicks, beans and shells on a grid. Have the students volunteer rules that they saw. Ask the students to look for rules as you carefully and silently model a two-digit addition problem without talking. Have them record what they saw. Share responses. Model once again silently. Share more ideas and rules. (Note - key rules are: five dots equals one bar, and four bars equals one dot in a higher place value.) Now model one last problem, explaining rules as you go. Ask for a student volunteer to model and review the Maya numerals from 1-19. Discuss place values in a base twenty system: “twenties”, “four hundreds” and “eight thousands”.

Students break up into small teams. Hand out Maya math grid and markers. Practice

another two-digit addition as a group. Have students complete the computational worksheet staying within the Maya system (ie they shouldn’t convert Maya numbers into decimal numbers).

When students demonstrate mastery have them convert the Maya vigesimal numbers to decimal numbers.

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Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

DIGGING DEEPER: MAYA CIVILIZATION 3

Conclusion: What method was most helpful to you in learning the Mayan numerals? Why? What is something you learned about our decimal system by exploring the vigesimal system? What is one strength of each system? What is one way the two systems are similar? What is an important difference?

How practical is the Maya number system? (What if you were an illiterate market trader writing in the dust, using sticks and stones to make your calculations?) Was it easier to calculate within the Maya system, or to convert the Maya numbers to the decimal system?

What are some of the challenges archeologists face as they attempt to

interpret ancient civilizations? (For instance, their information is frozen in time- snapshots instead of videos, written communication instead of demonstrated communication.)

ACTIVITY 2 DIFFERING NUMBERING SYSTEMS

Lead/Inquiry: List as many other number systems as possible: Chinese (base 10), binary (base 2), Babylonian (base 60), Maya (base 20), Egyptian (base 10) etc.

Procedure: Write suggestions on slips of paper, and have teams randomly select assignment to research. How does the number system work? Why was the system based on that particular number? What is the practical application of the system? What are its weaknesses? How does it compare to our own.

Students then present their number system to the rest of the class. Divide class into two groups: was math discovered or invented. Have each team

think of all the reasons they can to defend their side. Present arguments.

Expansion: Number systems are not confined to counting and arithmetic. Have the students write a response paper on the other number systems they encounter throughout the day, including telling time, calendar dates, handling money, etc. What number bases do these systems use? Why? How are they similar to or different from out way of counting?

Conclusion: What are three things you have learned about the process of mathematics? Do you think math was discovered or invented? Explain your answer.

Assessment: Students shall be assessed based upon their understanding of the mathematical concepts presented as demonstrated by their completion of written problem sets, group presentations, and their contributions to class discussions.

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Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

DIGGING DEEPER: MAYA CIVILIZATION 4

Attached Materials: - Maya number worksheet & key

- Maya addition and subtraction worksheet & key

- Math grid for modeling

- Maya math demonstration video (high and low resolution)

Useful Links: Ancient Math systems:

- http://www.jaguarstones.com/MayaMath.html

- http://en.wikipedia.org/wiki/History_of_mathematics

- http://www.math.wichita.edu/history/topics/num-sys.html

- http://www.youtube.com/watch?v=cy-8lPVKLIo

Maya math lesson plans:

- http://www.outreachworld.org/resource.asp?curriculumid=996

- www.exploratorium.edu/ancientobs/chichen/docs/Mayan_Math.pdf

WORKSHEET 1DECIPHERING MAYA NUMBERS

You are an archeologist who has discovered a Maya Codex covered in glyphs and Maya numbers. Your colleagues have been able to translate a few of the Maya numbers. Using the translated numbers, decipher the rest of the numerals.

TRANSLATED NUMERALS

a) = ______ b) = ______ c) = ______

d) = ______ e) = ______ f ) = ______

g) = ______ h) = ______ i) = ______

j) = ______ k) = ______ l) = ______

m) = ______ n) = ______ o) = ______

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Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

= 2 = 8 = 12 = 20 = 33

A portion of an Ancient Maya Almanac (The Dresden Codex)

WORKSHEET 1- KEYDECIPHERING MAYA NUMBERS

You are an archeologist who has discovered a Maya Codex covered in glyphs and Maya numbers. Your colleagues have been able to translate a few of the Maya numbers. Using the translated numbers, decipher the rest of the numerals.

TRANSLATED NUMERALS

a) = 3 b) = 5 c) = 13

d) = 0 e) = 9 f ) = 1

g) = 11 h) = 15 i) = 4

j) = 7 k) = 10 l) = 19

m) = 20 n) = 104 o) = 166

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Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

= 2 = 8 = 12 = 20 = 33

A portion of an Ancient Maya Almanac (The Dresden Codex)

www.jaguarstones.comDIGGING DEEPER: MAYA MATH 1

Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

WORKSHEET 2MAYA ADDITION & SUBTRACTION

Set up and solve the following equations using the provided materials.

=

+ =

+ +

- =- =

A) B)

C) D)

E) F)

+ =

_____ _____+ = _____

+ =

_____ _____+ = _____

_____ _____+ = _____

_____ _____- = _____ _____ _____- = _____

__________ _____++ = _____

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Copyright J&P Voelkel 2012. Not to be reproduced for sale or profit.

WORKSHEET 2 - KEYMAYA ADDITION & SUBTRACTION

Set up and solve the following equations using the provided materials.

=

+ =

+ +

- =- =

A) B)

C) D)

E) F)

+ =

224 150+ = 374

+ =

233 370+ = 603

278 133+ = 411

2,667 2,367- = 300 2,773 757- = 2,016

5355,173 1,212++ = 6,920

University of Colorado, Project EXTREMES

http://cires.colorado.edu/education/outreach/extremes/index.html Page 1

Lesson Title: Earthworks: The Combination of Art and Nature

NSF GK12 Fellow: Leigh Cooper (Boulder, CO)

Grade Level: All Middle School and Elementary School Sciences

Type of Lesson: STEM, Art

Objectives: 1) Learn about the Earthworks art movement, 2) Use observation skills to

find art in nature, 3) Create an Earthworks art piece that describes a scientific concept or

theory, and 4) Understand that scientists need to communicate with non-scientists and

science can be communicated through art.

Background Information: I like to use this lesson at the end of the year as a little bit of

review for students. The students then have a full year’s of science to draw from as

inspiration for their art piece. Also, it gets students outside when they are squirmy at the

end of the semester.

References:

Alba the Rabbit http://www.ekac.org/gfpbunny.html#gfpbunnyanchor

Earthworks Movement http://joshuasiegal.org/mfa/earthworks_report.pdf

http://en.wikipedia.org/wiki/Land_art

Earthworks pieces http://westvancouver.ca/Level2.aspx?id=33664

http://www.rwc.uc.edu/artcomm/web/w2005_2006/maria_Goldsworthy/TEST/index.html

http://boingboing.net/2008/01/30/spiral-jetty-monumen.html

http://flatrock.org.nz/topics/intellect_and_entertain/pink_water_white_salt_black_rock.htm

http://aloneone.wordpress.com/2008/09/24/andy-goldsworthy/

http://zero1blog.com/?p=598

http://jonathans-examined-life.blogspot.com/2009_05_01_archive.html

http://www.cloudyreason.com/blog-posts/we-love-land-art.html

http://www.micheldavo.com/land-art-01/land-art-01-04.html

Lesson Vocabulary: Earthworks (Land art, Earth art), ephemeral, erosion,

decomposition

Materials Required:

Slide show or pictures of example artwork

Digital camera with the capability to download and print the pictures

A 3x5 note card for each group

University of Colorado, Project EXTREMES

http://cires.colorado.edu/education/outreach/extremes/index.html Page 2

Preparation: 1) Create opening presentation about Earthworks, 2) Make sure camera is

in working order (enough memory, battery charged), and 3) Find an outdoor location

with enough variability in landscape that the students can spread out and find different

environments in which to create their works of art.

Safety Information: Be aware of the weather and warn the students to bring appropriate

clothing.

Engagement: Show students the picture of Alba, the fluorescent rabbit.

Art and science have been crossing paths for centuries. In this case an artist created a living art piece that sparked a conversation between artists, scientists, philosophers, and the general public about the implications of genetic engineering. We can teach about science through art, we can talk about science through art and we can create art through science. Can you think of any examples where art and science have been combined? Let students brainstorm for a few minutes. They can also think about literature, poetry, or movies and plays that have incorporated science into them. Exploration: Today, we will talk about a very specific art form called Earthworks. Earthworks (Land art, Earth art) is an art movement which began in the late 1960’s where the landscape and the artwork is intertwined. The artist uses natural materials such as stones, twigs, feathers, water, leaves, trees, bedrock, and the land to create a piece of artwork.

University of Colorado, Project EXTREMES

http://cires.colorado.edu/education/outreach/extremes/index.html Page 3

Some artists also incorporate manmade materials such as concrete, metal, and asphalt into the art piece. The art can range in size from incredibly large, for which the artist uses bulldozers and dynamite to create, or very small.

In 1970, the “Spiral Jetty” was created in the Great Salt Lake by Robert Smithson.

University of Colorado, Project EXTREMES

http://cires.colorado.edu/education/outreach/extremes/index.html Page 4

The artist used black basalt rocks and earth from the surrounding area to create a 1,500 feet long coil. The line of earth is 15 feet wide. The look of the jetty changes with the rise and fall of the surface water, which sometimes covers the art piece. For Earthworks, the sculpture is not set outside but the landscape is the base of the sculpture. Often change over time is incorporated into the art piece. The art piece may change as erosion (the process by which the surface of the earth is worn away by the action of water, glaciers, winds, waves, etc.) or decomposition (the physical breakdown of organic matter or the chemical break down of organic matter by bacteria, fungi, etc.) occurs. This means most Earthworks are ephemeral (lasting for only a short time, transitory, short-lived).

By Andy Goldworthy, These are only captured in photography. A number of famous Earthworks use shadows and reflections as part of their art.

The students’ assignment is three fold.

1) In groups of two or individually, they need to create an Earthworks piece of art that they will share with the class. These will be created outside.

2) The art piece should be inspired by a scientific idea, theory, or fact they have learned in school. (This can be expended to include human and nature interaction or environmental themes.)

3) The art piece should also have a title.

University of Colorado, Project EXTREMES

http://cires.colorado.edu/education/outreach/extremes/index.html Page 5

Once outside, the students should practice finding art in nature. You can choose one or both of the exercises. Give the students a defined area in which to range and a meeting place for after the exercise. A whistle is handy to bring the students back together.

1) A New View: Have the students look at the natural world from a different angle. Examples- Upside-down on their backs, from a lofty height. Have them share with a friend or the group patterns, colors, etc. that they have never noticed before.

2) Lilliputians’ Point of View: Have the students look very closely at the plants, rocks, etc that they would normally walk past very quickly. This may involve getting down on their hands and knees. Have them share with a friend or the group patterns, colors, textures, etc. that they have never noticed before.

At this point the groups should spread out and start brainstorming and building their project. This can take anywhere from 10-40 minutes depending on the age of the class and the class’ love of art. Explanation: When the art pieces are complete, each group will describe their art piece including their scientific theme and their title. The teacher should take a digital picture of the piece and the artist(s). Inside (possibly the next day), the pictures can be printed out from the digital camera and displayed. The students can fill out a notecard with the scientific theme, title, and artist’s names and it can be posted next to the art piece. Evaluation: Ask the students why is it important for scientists to explain scientific ideas

to non-scientists. (Answer: Many things that scientists discover, like how to keep our

water clean or how to save energy, affect every single human being, and if scientists only

talk to other scientists or don’t know how to tell others about their ideas, we will not

know how to keep our water clean or save energy.)

Can they think of examples of when scientists interact with the public? (Answer: Climate

change, weather, earthquakes, tsunamis, volcanoes, inventors such as those that make the

energy efficient cars and their iPhones, to name a few).

Do the students think they could teach someone who had never learned about their

“scientific theme” about science through their art piece? (Hopefully, because the take

home message is “science can be communicated through art”. Scientists can use many

forms of communication to teach about science including art, literature, poetry, and the

theater or movies.)

Wrap-up: If there is time, it is also interesting to visit the art pieces a week after the lesson is completed and see how the art pieces have faired. It drives home the ephemeral quality of the artwork.

This module aims to introduce Precalculus high school students to the basic capabilities of Matlab by using functions. Matlab will be used in subsequent modules to help to teach research related concepts or to help emphasize classroom learning. This Introduction to Matlab package includes a lesson plan, a PowerPoint presentation, a  worksheet and a reference sheet. 

Science Lesson Plan Teacher:

*This template is available in electronic form. 1

Period: Class: AP Precalc Date(s): Lesson # 1 Introduction to Matlab using Functions SETTING THE STAGE Essential Question

How to visualize functions, their domain and range?

Content Objective(s) (Student-friendly)

Introduces basic Matlab commands for creating functions, defining variables and specifying their domain. Visualization through one-dimensional plots will also be introduced, to compare different functions.

Connection to previous or future lessons

Material in this lesson plan will serve as a background for future lessons which will be used to show Precalculus concepts in an alternate way and to demonstrate research related concepts.

Critical Thinking Questions

What is the importance of knowing what the graphical representation of a function looks like? What are some benefits of being able to manipulate the scale of a graph?

Key Vocabulary • Variables • Functions • Scale • Domain

• Range • Maxima • Minima • Linear

Materials Needed/Safety

Computers with Matlab software Matlab reference guide. Matlab code

ACTIVE INSTRUCTION

• Launch (Engage)

Display some 2-d or 3-d visualization from Matlab using an existing demo application. Ask students questions about what they see and how they think this was generated. Explain briefly what the simulation is about and give them a hands on activity where they can change some parameter of this application and see a difference. Students will also see a short vide titled “Matlab is Cool” The intention of showing the video is to convey other students’ excitement for a software tool like Matlab

Science Lesson Plan Teacher:

*This template is available in electronic form. 2

• Investigation (Explore)

Following the launch, students will be introduced to some basic commands and will learn how create a basic linear function and its graph. F(x)=2x+3 They will later be asked to change the slope of the function the will be asked what changes they notices when the slope changes. Students will not be told that the coefficient in front of x is the slope. They will be asked to describe the graph in terms of decrease or increase and rate of change.

TIME FOR REFLECTION

• Summarization (Explain & Extend)

We will discuss the importance of being able to find the domain and range of a function with an appropriate scale for graphing. If time permits students will be asked to compare the functions G(x) = 3x^2, x<1 F(x) = 3x^2, x>1 Discuss the use of simulation and how it is helpful to visualize the data. Explain thoroughly the plot that was generated. Explain what is to be presented next class. Ask the students to identify what was the most useful component in the computational exercises. Discuss why and how the students would use the software. Ask the students to note their observations in their journals.

• Assessment (Evaluate)

Written notes in their journals will be reviewed.

• Homework

Using Matlab to Plot Functions 

Name: ___________________________                                                                   Date:_______________ 

First identify the grandmother function, then plot and  describe the transformation of the following functions: 

Grandmother Function  Function  1  Function 2   2  3 2 

         

  4| | |12 

          

| 

  2 5   10 5             

 

 

M-Files New M-Files File → New → M-File (opens blank page) Open M-Files File → Open → Select a desired M-File → Click Open Save M-Files New File → Save As…→ Select a folder where you want to save your new M-File Old File → Save (Ctrl + S)

Vectors Data Stored as Vectors and Matrices Row vector A = [1 2 3 4]; leave space between each number. This generates 1 x 4 row vector Column vector B = [1; 2; 3; 4]; add semicolon(;) between each number. This generates 4x1 column vector Example: 3 x 2 Matrix C = [ 1 2; 3 4; 5 6] = [ 1 2 3 4 5 6]

Plot 2D plot plot(x,y) → plots a graph of y = f(x) Label Note: first plot a graph than label it xlabel(‘x-axis’) → labels x-axis, make sure open and close the parenthesis, and add single quotation mark at the beginning and at the end. ‘x-axis’ ylabel(‘y-axis’) → labels y-axis title(‘y vs. x’) → to display a title at the top location of the graph legend(‘y = f(x)’); → describes the figure

Subplot Used to represents multiple graphs in single page subplot(2,3,4); → Used to place plots on same page: subplot(r,c,i) i =1 , 2, ….r x c r=row c=column i=placement of graph Note: First use subplot command then repeat plot, xlabel, ylabel etc. for every subplots. subplot(2,3,1);plot(x1,y1); xlabel(‘….’) …….

subplot(2,3,2);plot(x2,y2); xlabel(‘….’) …….

subplot(2,3,3);plot(x3,y3); xlabel(‘….’) …….

LineSpec Arguments for plot Line Style - Solid line (default)

-- Dashed line : Dotted line -. Dash-dot line

Marker + Plus sign o Circle * Asterisk . Point x Cross s Square d Diamond ^ Upward pointing triangle > Right pointing triangle < Left pointing triangle p Five-pointed star (pentagon) h Six-pointed star (hexagon) Color r Red g Green b Blue c Cyan m Magenta y Yellow k Black w White

M-Files Plot LineSpec Arguments for plot

Command Window

Matlab Desktop

Details

Workspace

Command History

Current Directory

Sample code %define a variable x as a 1X4 %vector that contains the numbers % 1 through 4 x = [1 2 3 4] % find the dimensions of the vector size(x) %find the length of the row vector length(x)

Random Numbers

normrnd syntax R= normrnd(mu,sigma,m,n) Description Generates random numbers from the normal distribution with mean parameter mu and standard deviation parameter sigma, where scalars m and n are the row and column dimensions of R Example R= normrnd([1 2 3 ;4 5 6],0.1,3.2) R= 0.9299 1.9361 2.9640 4.1246 5.0577 5.9864 randn Description Generates a set of pseudorandom numbers from a standard normal distribution randint syntax out = randint(m,n,rg) Description

2D plot hist state