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# Reflections on a 119 Year-old Curriculum

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Tweet## Nils Ahbel

on 29 June 2011#### Transcript of Reflections on a 119 Year-old Curriculum

1892 2011 Examples of a Relevant Curriculum What was US math curriculum like in... A Mathematics Curriculum Report Card for... Charting a new course ... Reflections on a

119 Year-Old Curriculum

Presenter: Nils Ahbel http://books.google.com/books?id=pfAGAAAAYAAJ&printsec=frontcover&dq=an+exercise+book+in+algebra+mccurdy&source=bl&ots=zHUGZYI0CV&sig=k-FNeGJY52GxaENDS5ciVPPdYZo&hl=en&ei=5_QVTbG7OYGBlAfgzNTTCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBMQ6AEwAA#v=onepage&q&f=false 1892 - Committee of Ten 1900 - World population = 1.5 billion 1903 - Airplane 1923 - TV/Cathode ray tube 1928 - Antibiotics 1951 - Credit card 1955 - Oil overtakes coal as #1 energy source 1990 - World Wide Web http://www.answers.com/topic/phillips-exeter-academy http://www.google.com/imgres?imgurl=http://www.who2.com/blog/assets_c/2011/02/bookeraanew-thumb-450x450-1160.jpg&imgrefurl=http://www.who2.com/blog/2011/02/black-history-month-biography-booker-t-washington.html&usg=__0PFAmNIZSBri3asQsePaSiwPNDc=&h=450&w=450&sz=104&hl=en&start=0&zoom=1&tbnid=bKWcejnOdXW9ZM:&tbnh=133&tbnw=133&ei=SveBTcTjHsuSgQfO1_DDCA&prev=/images%3Fq%3Deliot%2Bbooker%2Bt%2Bwashington%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26hs%3DzgC%26sa%3DN%26rls%3Dorg.mozilla:en-US:official%26biw%3D1260%26bih%3D723%26tbs%3Disch:10%2C146&um=1&itbs=1&iact=hc&vpx=456&vpy=226&dur=588&hovh=225&hovw=225&tx=122&ty=104&oei=SveBTcTjHsuSgQfO1_DDCA&page=1&ndsp=28&ved=1t:429,r:16,s:0&biw=1260&bih=723 Education in the late 1800s, for the most part followed the European model

In 1892 The National Education Association formed

The Committee of Ten

The recommendations of the Committee of Ten... * 8 years of Elementary and 4 years of High School

* Reduce number of subjects to about 5

* Biology in 9th or 10th, Chemistry in 11th, and Physics in 12th

* Algebra in 9th grade, Geometry in 10th, Trigonometry in 12th

* All students should take a college prep curriculum Statistics Linear to Exponetial LARGE/small Numbers Normal Distribution Recursion Simulation and Probability Recursion Recursion Blood alcohol content or BAC is typically measured in mg of alcohol /ml of blood. Adults over 21 in most states will be arrested for DUI if they have more than 80 mg/ 100 ml or 0.08% BAC. Many handheld BAC meters like the AlcoHAWK Elite Digital by Breathalyzer and the Alco-Sensor III by Intoximeters give a readout to three decimal places. According to a Clinical Chemistry article, the standard deviation for a new Model 1000 Breathalyzer is 0.0037. Let’s say you are on a jury in which the defendant is charged for DUI and the BAC was measured to be exactly 0.080 which is the minimum amount necessary for a conviction.

a. What is the probability that the defendant would have a measured BAC of 0.080 or greater if

in fact the defendant’s actual BAC was 0.079?

b. What is the probability that the defendant would have a measured BAC of 0.080 or greater if

in fact the defendant’s actual BAC was 0.075?

c. What is the probability that the defendant would have a measured BAC of 0.080 or greater if

in fact the defendant’s actual BAC was 0.070?

d. Based on the evidence, describe whether you think it was safe for the defendant to be

driving. Explain. (If you weigh 160 lbs. and drink three 12 oz. beers in succession, your

BAC would be about 0.070)

e. Based on the evidence, describe whether you think the defendant should be found guilty of

DUI. Explain.

Sources:

•Breath-tester. Breath Alcohol Testers, http://www.breath-tester.com/, 3/17/2009

•Wikipedia, BAC, http://en.wikipedia.org/wiki/Blood_alcohol_content, 3/17/2009

•G. Simpson, Accuracy and ZPresicion of Breath-Alcohol Measurements for a Random Subject in the Postabsorptive State, Clinical Chemistry, 33/2, 261-268, 1987 (http://www.clinchem.org/cgi/reprint/33/2/261.pdf) As opposed to Linear to Polynomial 1989 - The "Standards" http://www.usi.edu/science/math/sallyk/Standards/Previous/CurrEvStds/currstand9-12.htm SUMMARY OF CHANGES IN CONTENT AND EMPHASES IN 9-12 MATHEMATICS

TOPICS TO RECEIVE INCREASED ATTENTION

ALGEBRA

* The use of real-world problems to motivate and apply theory

* The use of computer utilities to develop conceptual understanding

* Computer-based methods such as successive approximations and graphing utilities for solving equations and inequalities

* The structure of number systems

* Matrices and their applications

GEOMETRY

* Integration across topics at all grade levels

* Coordinate and transformation approaches

* The development of short sequences of theorems

* Deductive arguments expressed orally and in sentence or paragraph form

* Computer-based explorations of 2-D and 3-D figures

* Three-dimensional geometry

* Real-world applications and modeling

TRIGONOMETRY

* The use of appropriate scientific calculators

* Realistic applications and modeling

* Connections among the right triangle ratios, trigonometric functions, and circular functions

* The use of graphing utilities for solving equations and inequalities

FUNCTIONS

* Integration across topics at all grade levels

* The connections among a problem situation, its model as a function in symbolic form, and the graph of that function

* Function equations expressed in standardized form as checks on the reasonableness of graphs produced by graphing utilities

* Functions that are constructed as models of real-world problems

STATISTICS

PROBABILITY

DISCRETE MATHEMATICS High school drop outs Math "drop outs" What society has to say "The role of the cartoonist, as well as making us laugh at our shared predicament, is to discover and express what is repressed, and to say out loud what people everywhere are whispering". Michael Leunig http://www.abc.net.au/mediawatch/transcripts/s1317984.htm http://www.google.com/imgres?imgurl=http://www.all4ed.org/files/DF_01_1.jpg&imgrefurl=http://www.all4ed.org/about_the_crisis/promotingpower&usg=__lSlf3rpVnaLTyoiJ3ngdCoWn2eE=&h=735&w=1125&sz=381&hl=en&start=0&sig2=cZyBGMWqMftg1Pru1izFEw&zoom=1&tbnid=RqNCLorn8CF_SM:&tbnh=145&tbnw=222&ei=CVYbTbSSOIa8lQfMzpjeAg&prev=/images%3Fq%3Ddrop%2Bout%2Bfactory%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26biw%3D1143%26bih%3D656%26tbs%3Disch:1&um=1&itbs=1&iact=rc&dur=638&oei=CVYbTbSSOIa8lQfMzpjeAg&esq=1&page=1&ndsp=12&ved=1t:429,r:0,s:0&tx=75&ty=57 Trends in High School Dropout and Completion Rates in the US: 1972–2008 (Dec 2010)

National averaged freshman graduation rate for public school students the class of 2007–08 was 74.9%. http://nces.ed.gov/pubs2011/2011012.pdf 14.1% of graduating seniors had taken a class that was called "calculus." US Department of Education. 2009. Education Longitudinal Study of 2002

nces.ed.gov/surveys/ELS2002/ 52% of them took an AP Calculus exam. professionals.collegeboard.com/data-reports-research/ap The statistics below and more are found in a great article...

AP Calculus: What We Know David M. Bressoud June, 2009 http://www.maa.org/columns/launchings/launchings_06_09.html 83%* of them earned a 3 or higher on the AP exam *192,000/225,000 from http://www.maa.org/columns/launchings/launchings_06_09.html So, 10.6% (14.1% of 74.9%) of high school age students take "calculus" So, 5.5% (52% of 10.6%) of high school age students take an AP exam So, 4.6% (83% of 5.5%) of high school age students pass the AP exam http://www.maa.org/features/faceofcalculus.html 60% of college students who take calculus, pass Estimate from the graph at the right Wilson, R. (1997). A decade of teaching reform Calculus’ has been a disaster, critics charge. Chronicle of Higher Education, 43(22), A12-A13. 6.1% of high school graduates take Calculus in college So, 3.6% (60% of 6.1%) of college students pass calculus About 8.2%(4.6% + 3.6%) of the population pass calculus Photo: Lucia Suarez Sang Characteristics of a Relevant Curriculum Utilized

Day-to-day

College Designed for the Majority Dynamic

Virtual resources

Instead of textbooks Less is More

Captivating problems

Not 1-31 odd, 43 Open Content

Free! http://www.google.com/imgres?imgurl=http://everythingmustgo.org/wp-content/uploads/2011/01/FirstCreditCard.jpg&imgrefurl=http://everythingmustgo.org/&usg=__2PP8IEfMruWd4U4d_Wip137yTWs=&h=317&w=539&sz=33&hl=en&start=0&zoom=1&tbnid=zkc6EkkpTkfyOM:&tbnh=99&tbnw=168&ei=L-WBTdrpNdLqgQej2JXNCA&prev=/images%3Fq%3Dthe%2Bfirst%2Bcredit%2Bcard%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26hs%3D0nq%26sa%3DX%26rls%3Dorg.mozilla:en-US:official%26biw%3D1260%26bih%3D723%26tbs%3Disch:1&um=1&itbs=1&iact=hc&vpx=286&vpy=101&dur=79&hovh=172&hovw=293&tx=153&ty=93&oei=--SBTaarIYrfgQecoanaCA&page=1&ndsp=24&ved=1t:429,r:1,s:0 http://dictionary.reference.com/browse/esoteric http://dictionary.reference.com/browse/exoteric http://www.etsy.com/listing/25676713/vintage-medicine-bottles-from-the-1930s http://www.tvworthwatching.com/blog/2008/07/tvs-digital-conversion-what-wi-1.shtml http://www.google.com/imgres?imgurl=http://assets.theatlantic.com/static/mt/assets/international/kuwait1950.jpg&imgrefurl=http://www.theatlantic.com/international/archive/2010/04/the-upside-of-depending-on-foreign-oil/38380/&usg=__LwV2APr8i5ufk7iH22lXBusz_a8=&h=400&w=600&sz=256&hl=en&start=0&zoom=1&tbnid=pdTr6BthiJncxM:&tbnh=147&tbnw=206&ei=mOyBTd2xBsnagQfalozRCA&prev=/images%3Fq%3Dhistory%2Bof%2Boil%2Bdrilling%2B1950s%26hl%3Den%26client%3Dfirefox-a%26hs%3DRJr%26rls%3Dorg.mozilla:en-US:official%26biw%3D1260%26bih%3D723%26tbs%3Disch:10%2C229&itbs=1&iact=hc&vpx=134&vpy=305&dur=2056&hovh=183&hovw=275&tx=118&ty=78&oei=mOyBTd2xBsnagQfalozRCA&page=1&ndsp=24&ved=1t:429,r:18,s:0&biw=1260&bih=723 http://www.google.com/imgres?imgurl=http://3.bp.blogspot.com/_-5pQYFqkNjE/TKdq9gZfJ0I/AAAAAAAAANc/Ae_W1gYl9ec/s1600/ViolaWWW.png&imgrefurl=http://doylielife.blogspot.com/2010_10_01_archive.html&usg=__mYAbvO7TBBi0YdT_d4ZhFqgHXvo=&h=492&w=594&sz=10&hl=en&start=0&zoom=1&tbnid=Yh1UoDU-91_13M:&tbnh=156&tbnw=188&ei=6_OBTd52iN-BB6ed6cYI&prev=/images%3Fq%3Dimages%2Bof%2Bviola%2Bweb%2Bbrowser%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26hs%3D4SC%26rls%3Dorg.mozilla:en-US:official%26biw%3D1260%26bih%3D723%26tbs%3Disch:1&um=1&itbs=1&iact=hc&vpx=534&vpy=202&dur=1211&hovh=204&hovw=247&tx=114&ty=120&oei=6_OBTd52iN-BB6ed6cYI&page=1&ndsp=18&ved=1t:429,r:2,s:0 N:\$ My Documents on FacStaff\Presentations\Exeter\2011\Evening talk\Airplane.png http://www.dimensional.com/famafrench/2009/05/how-unusual-was-the-stock-market-of-2008.html http://www.diabetesmonitor.com/m57.htm http://www.touchbriefings.com/pdf/1479/Hirsch.pdf https://dalearn.deerfield.edu/course/view.php?id=1038&topic=0#section-1 100 meter dash video link below https://dalearn.deerfield.edu/course/view.php?id=1038&topic=0#section-9 FST: Problem Set 9-1, #2 FST: Problem Set 1-8 FST: Problem Set 9-4, #2 http://finance.yahoo.com/echarts http://www.gapminder.org/world/#$majorMode=chart$is;shi=t;ly=2003;lb=f;il=t;fs=11;al=30;stl=t;st=t;nsl=t;se=t$wst;tts=C$ts;sp=5.59290322580644;ti=2009$zpv;v=0$inc_x;mmid=XCOORDS;iid=phAwcNAVuyj1jiMAkmq1iMg;by=ind$inc_y;mmid=YCOORDS;iid=phAwcNAVuyj2tPLxKvvnNPA;by=ind$inc_s;uniValue=8.21;iid=phAwcNAVuyj0XOoBL_n5tAQ;by=ind$inc_c;uniValue=255;gid=CATID0;by=grp$map_x;scale=log;dataMin=295;dataMax=79210$map_y;scale=lin;dataMin=19;dataMax=86$map_s;sma=49;smi=2.65$cd;bd=0$inds=i101_l001800b6at;i44_l001800b7aG;i239_l001800cHaO;modified=75 http://www.federalreserve.gov/creditcardcalculator/Default.aspx http://www.mathcurriculumcenter.org/PDFS/CCM/summaries/comm_of_10_summary.pdf www.youtube.com/watch?v=ilWaefe6bK4&feature=related http://hamsnetwork.org/metabolism/ Linear decay Exponential decay Metabolism of Alcohol (linear)

Versus Most Drugs (exponential) http://www.duifighters.com/alcohol-metabolism/ Emphasize Demphasize How Unusual Was the Stock Market of 2008? 10, 12, 14, 16, ... It’s as if we were English teachers teaching only Shakespeare and Grammar. ~10% of SAT II, Math Level I&II are Probability and Statistics Less More This presentation available at www.ahbel.com under "Past Presentations" Time out!

For which student population is this intended?

Full transcript119 Year-Old Curriculum

Presenter: Nils Ahbel http://books.google.com/books?id=pfAGAAAAYAAJ&printsec=frontcover&dq=an+exercise+book+in+algebra+mccurdy&source=bl&ots=zHUGZYI0CV&sig=k-FNeGJY52GxaENDS5ciVPPdYZo&hl=en&ei=5_QVTbG7OYGBlAfgzNTTCw&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBMQ6AEwAA#v=onepage&q&f=false 1892 - Committee of Ten 1900 - World population = 1.5 billion 1903 - Airplane 1923 - TV/Cathode ray tube 1928 - Antibiotics 1951 - Credit card 1955 - Oil overtakes coal as #1 energy source 1990 - World Wide Web http://www.answers.com/topic/phillips-exeter-academy http://www.google.com/imgres?imgurl=http://www.who2.com/blog/assets_c/2011/02/bookeraanew-thumb-450x450-1160.jpg&imgrefurl=http://www.who2.com/blog/2011/02/black-history-month-biography-booker-t-washington.html&usg=__0PFAmNIZSBri3asQsePaSiwPNDc=&h=450&w=450&sz=104&hl=en&start=0&zoom=1&tbnid=bKWcejnOdXW9ZM:&tbnh=133&tbnw=133&ei=SveBTcTjHsuSgQfO1_DDCA&prev=/images%3Fq%3Deliot%2Bbooker%2Bt%2Bwashington%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26hs%3DzgC%26sa%3DN%26rls%3Dorg.mozilla:en-US:official%26biw%3D1260%26bih%3D723%26tbs%3Disch:10%2C146&um=1&itbs=1&iact=hc&vpx=456&vpy=226&dur=588&hovh=225&hovw=225&tx=122&ty=104&oei=SveBTcTjHsuSgQfO1_DDCA&page=1&ndsp=28&ved=1t:429,r:16,s:0&biw=1260&bih=723 Education in the late 1800s, for the most part followed the European model

In 1892 The National Education Association formed

The Committee of Ten

The recommendations of the Committee of Ten... * 8 years of Elementary and 4 years of High School

* Reduce number of subjects to about 5

* Biology in 9th or 10th, Chemistry in 11th, and Physics in 12th

* Algebra in 9th grade, Geometry in 10th, Trigonometry in 12th

* All students should take a college prep curriculum Statistics Linear to Exponetial LARGE/small Numbers Normal Distribution Recursion Simulation and Probability Recursion Recursion Blood alcohol content or BAC is typically measured in mg of alcohol /ml of blood. Adults over 21 in most states will be arrested for DUI if they have more than 80 mg/ 100 ml or 0.08% BAC. Many handheld BAC meters like the AlcoHAWK Elite Digital by Breathalyzer and the Alco-Sensor III by Intoximeters give a readout to three decimal places. According to a Clinical Chemistry article, the standard deviation for a new Model 1000 Breathalyzer is 0.0037. Let’s say you are on a jury in which the defendant is charged for DUI and the BAC was measured to be exactly 0.080 which is the minimum amount necessary for a conviction.

a. What is the probability that the defendant would have a measured BAC of 0.080 or greater if

in fact the defendant’s actual BAC was 0.079?

b. What is the probability that the defendant would have a measured BAC of 0.080 or greater if

in fact the defendant’s actual BAC was 0.075?

c. What is the probability that the defendant would have a measured BAC of 0.080 or greater if

in fact the defendant’s actual BAC was 0.070?

d. Based on the evidence, describe whether you think it was safe for the defendant to be

driving. Explain. (If you weigh 160 lbs. and drink three 12 oz. beers in succession, your

BAC would be about 0.070)

e. Based on the evidence, describe whether you think the defendant should be found guilty of

DUI. Explain.

Sources:

•Breath-tester. Breath Alcohol Testers, http://www.breath-tester.com/, 3/17/2009

•Wikipedia, BAC, http://en.wikipedia.org/wiki/Blood_alcohol_content, 3/17/2009

•G. Simpson, Accuracy and ZPresicion of Breath-Alcohol Measurements for a Random Subject in the Postabsorptive State, Clinical Chemistry, 33/2, 261-268, 1987 (http://www.clinchem.org/cgi/reprint/33/2/261.pdf) As opposed to Linear to Polynomial 1989 - The "Standards" http://www.usi.edu/science/math/sallyk/Standards/Previous/CurrEvStds/currstand9-12.htm SUMMARY OF CHANGES IN CONTENT AND EMPHASES IN 9-12 MATHEMATICS

TOPICS TO RECEIVE INCREASED ATTENTION

ALGEBRA

* The use of real-world problems to motivate and apply theory

* The use of computer utilities to develop conceptual understanding

* Computer-based methods such as successive approximations and graphing utilities for solving equations and inequalities

* The structure of number systems

* Matrices and their applications

GEOMETRY

* Integration across topics at all grade levels

* Coordinate and transformation approaches

* The development of short sequences of theorems

* Deductive arguments expressed orally and in sentence or paragraph form

* Computer-based explorations of 2-D and 3-D figures

* Three-dimensional geometry

* Real-world applications and modeling

TRIGONOMETRY

* The use of appropriate scientific calculators

* Realistic applications and modeling

* Connections among the right triangle ratios, trigonometric functions, and circular functions

* The use of graphing utilities for solving equations and inequalities

FUNCTIONS

* Integration across topics at all grade levels

* The connections among a problem situation, its model as a function in symbolic form, and the graph of that function

* Function equations expressed in standardized form as checks on the reasonableness of graphs produced by graphing utilities

* Functions that are constructed as models of real-world problems

STATISTICS

PROBABILITY

DISCRETE MATHEMATICS High school drop outs Math "drop outs" What society has to say "The role of the cartoonist, as well as making us laugh at our shared predicament, is to discover and express what is repressed, and to say out loud what people everywhere are whispering". Michael Leunig http://www.abc.net.au/mediawatch/transcripts/s1317984.htm http://www.google.com/imgres?imgurl=http://www.all4ed.org/files/DF_01_1.jpg&imgrefurl=http://www.all4ed.org/about_the_crisis/promotingpower&usg=__lSlf3rpVnaLTyoiJ3ngdCoWn2eE=&h=735&w=1125&sz=381&hl=en&start=0&sig2=cZyBGMWqMftg1Pru1izFEw&zoom=1&tbnid=RqNCLorn8CF_SM:&tbnh=145&tbnw=222&ei=CVYbTbSSOIa8lQfMzpjeAg&prev=/images%3Fq%3Ddrop%2Bout%2Bfactory%26um%3D1%26hl%3Den%26client%3Dfirefox-a%26rls%3Dorg.mozilla:en-US:official%26biw%3D1143%26bih%3D656%26tbs%3Disch:1&um=1&itbs=1&iact=rc&dur=638&oei=CVYbTbSSOIa8lQfMzpjeAg&esq=1&page=1&ndsp=12&ved=1t:429,r:0,s:0&tx=75&ty=57 Trends in High School Dropout and Completion Rates in the US: 1972–2008 (Dec 2010)

National averaged freshman graduation rate for public school students the class of 2007–08 was 74.9%. http://nces.ed.gov/pubs2011/2011012.pdf 14.1% of graduating seniors had taken a class that was called "calculus." US Department of Education. 2009. Education Longitudinal Study of 2002

nces.ed.gov/surveys/ELS2002/ 52% of them took an AP Calculus exam. professionals.collegeboard.com/data-reports-research/ap The statistics below and more are found in a great article...

AP Calculus: What We Know David M. Bressoud June, 2009 http://www.maa.org/columns/launchings/launchings_06_09.html 83%* of them earned a 3 or higher on the AP exam *192,000/225,000 from http://www.maa.org/columns/launchings/launchings_06_09.html So, 10.6% (14.1% of 74.9%) of high school age students take "calculus" So, 5.5% (52% of 10.6%) of high school age students take an AP exam So, 4.6% (83% of 5.5%) of high school age students pass the AP exam http://www.maa.org/features/faceofcalculus.html 60% of college students who take calculus, pass Estimate from the graph at the right Wilson, R. (1997). A decade of teaching reform Calculus’ has been a disaster, critics charge. Chronicle of Higher Education, 43(22), A12-A13. 6.1% of high school graduates take Calculus in college So, 3.6% (60% of 6.1%) of college students pass calculus About 8.2%(4.6% + 3.6%) of the population pass calculus Photo: Lucia Suarez Sang Characteristics of a Relevant Curriculum Utilized

Day-to-day

College Designed for the Majority Dynamic

Virtual resources

Instead of textbooks Less is More

Captivating problems

Not 1-31 odd, 43 Open Content

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Versus Most Drugs (exponential) http://www.duifighters.com/alcohol-metabolism/ Emphasize Demphasize How Unusual Was the Stock Market of 2008? 10, 12, 14, 16, ... It’s as if we were English teachers teaching only Shakespeare and Grammar. ~10% of SAT II, Math Level I&II are Probability and Statistics Less More This presentation available at www.ahbel.com under "Past Presentations" Time out!

For which student population is this intended?