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National Center for Education and the Economy

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Subject Matter Texts: Mathematics Found in Textbooks containing CCSSM domains for subject matter courses studied

Subject Matter Texts: Mathematics Found in Textbooks containing CCSSM domains for subject matter courses studied

National Center for Education and the Economy

Mathematics Panel

Co-ChairsPhilip Daro

Solomon Garfunkel

Panel

John T Baldwin

Patrick Callahan Andrew S Chen

Wade Ellis, Jr.

Robert L Kimball, Jr.

Lucy Hernandez Michal

Geri Anderson-Nielsen

Lisa Seidman

Colin L Starr

College and Career Readiness

With the growing complexity of the world and the increasing demands of the 21st-century workforce, there is little question that all students should be prepared for college, careers, and life.

The question is

… What does college and career-ready mean?

About 40 years ago, 72% of U.S. jobs were held by individuals with a high school degree or less.

By 2018, only 38% of jobs will be available to individuals without some education and training after high school.

Carnevale, Anthony P. et al. (June 2010). Help Wanted: Projections of Jobs and Education Requirements Through 2018. Georgetown. Center on Education and the Workforce

Nearly one-half of all job openings in the United States are “middle skill” jobs, all of which require at least some postsecondary education and training.

By contrast, those with a high school diploma or less are eligible only for one-fifth of all job openings,those that are deemed “low skill.”

Holzer, Harry J. and Robert I. Lerman (February 2009). The Future of Middle-Skill Jobs. Brookings Institution.

As our economy continues to shift from “middle skill” jobs, a goods-based to a knowledge-based economy, a greater proportion of the workforce will need some form of college degree or certification in order to succeed.

Of the 20 fastest-growing professions, 12 require an associate’s degree or higher, and of the 71 jobs projected to grow by 20% or more in the coming years, all of them will require some college.

Andrew Wiley, JeffreyWyatt andWayneJ. Camara. (2010). The DevelopmentofaMultidimensionalCollegeReadiness. TheCollegeBoard,

Occupations with the most job growth “middle skill” jobs,

(thousands of workers from 2012 through 2022)

Personal care aids 581

Registered nurses 527

Retail salespersons 435

Food (serve & prepare) 424

Nursing assistants 312

Administrative assistants 308

Customer service reps 299

Janitors 280

Construction laborers 260

General managers 244

Material handlers 242

Carpenters 218

Bookkeeping & accounting 205

Truck drivers 193

Medical secretaries 189

Childcare workers 184

Bureau of Labor Statistics: http://www.bls.gov/emp/ep_table_104.htm

The College Board: “ “middle skill” jobs, bigfuture” https://bigfuture.collegeboard.org/explore-careers/careers/industries-with-the-fastest-and-biggest-growth

The College Board: “ “middle skill” jobs, bigfuture” https://bigfuture.collegeboard.org/explore-careers/careers/industries-with-the-fastest-and-biggest-growth

a “middle skill” jobs, key role of two-year colleges:getting students career ready

core academic skills and the ability to apply those skills to concrete situations in order to function in the workplace and in routine daily activities

employability skills (such as critical thinking and responsibility) that are essential in any career area

technical, job-specific skills related to a specific career pathway

Association for Career and Technical Education • 1410 King Street, Alexandria, VA 22314

The question is “middle skill” jobs,

… What does college and career-ready mean?

Textbooks “middle skill” jobs,

Exams

Projects

Syllabi

AccountingAutomotive TechnologyBiotechElectrical TechnologyBusinessCriminal JusticeEarly Childhood EducationInformation Technology/Computer ProgrammingNursingGeneral Education Track

PISA Rubric

CCSS Content

Common Core “middle skill” jobs,

Grades 6 & 7

- Ratios & Proportional Relationships
- The Number System
- Expressions & Equations
- Geometry
- Statistics & Probability

Grade 8

- The Number System
- Expressions & Equations
- Functions
- Geometry
- Statistics & Probability

Subject Matter Texts: Percent of text chapters and exams containing CCSSM domains for subject matter courses studied

Chart 1

Subject Matter Texts: Mathematics Found in Textbooks containing CCSSM domains for subject matter courses studied

Page 14 - Figure 1

Subject Matter Texts: Mathematics Found in Textbooks containing CCSSM domains for subject matter courses studied

Page 16 - Figure 2.3

Subject Matter Texts: Mathematics Found in Textbooks containing CCSSM domains for subject matter courses studied

Page 17 - Figure 9.1

Page 19 - Figure 7

Page 19 – Figures 8 & 9

Mathematical Sciences: 2025 containing CCSSM domains for subject matter courses studied

Many mathematical scientists remain unaware of the expanding role for their field, and this incognizance will limit the community’s ability to produce broadly trained students and to attract more of them. A community-wide effort to rethink the mathematical sciences curriculum at universities is needed.

Page 2

Using mathematics in context – requiring reasoning and sense making

The PISA demands students to think about the mathematics they are working with by making connections and reflecting on them at a level beyond the routine use of mathematics. They are akin to the mathematical practices in the CCSS.

The panel found that only 10 to 15% of the items in texts and exams required this higher level of mathematical thinking.

Yet, all the mathematics found in core courses is IN CONTEXT. Math courses must prepare students for contextually-based problems for which the learner decides on the tools.

Standard 1: Make sense of problems and persevere in solving them

Standard 2: Reason abstractly and quantitatively

Standard 3: Construct viable arguments and critique the reasoning of others

Standard 4: Model with mathematics

Standard 5: Use appropriate tools strategically

Standard 6: Attend to precision

Standard 7: Look for and make use of structure

Standard 8: Look for and express regularity in repeated reasoning

Using mathematics in context – requiring reasoning and sense making

The PISA demands students to think about the mathematics they are working with by making connections and reflecting on them at a level beyond the routine use of mathematics. They are akin to the mathematical practices in the CCSS.

The panel found that only 10 to 15% of the items in texts and exams required this higher level of mathematical thinking.

Yet, all the mathematics found in core courses is IN CONTEXT. Math courses must prepare students for contextually-based problems for which the learner decides on the tools.

Standard 1: Make sense of problems and persevere in solving them

Standard 2: Reason abstractly and quantitatively

Standard 3: Construct viable arguments and critique the reasoning of others

Standard 4: Model with mathematics

Standard 5: Use appropriate tools strategically

Standard 6: Attend to precision

Standard 7: Look for and make use of structure

Standard 8: Look for and express regularity in repeated reasoning

Using mathematics in context – requiring reasoning and sense making

The PISA demands students to think about the mathematics they are working with by making connections and reflecting on them at a level beyond the routine use of mathematics. They are akin to the mathematical practices in the CCSS.

The panel found that only 10 to 15% of the items in texts and exams required this higher level of mathematical thinking.

Yet, all the mathematics found in core courses is IN CONTEXT. Math courses must prepare students for contextually-based problems for which the learner decides on the tools.

Standard 1: Make sense of problems and persevere in solving them

Standard 2: Reason abstractly and quantitatively

Standard 3: Construct viable arguments and critique the reasoning of others

Standard 4: Model with mathematics

Standard 5: Use appropriate tools strategically

Standard 6: Attend to precision

Standard 7: Look for and make use of structure

Standard 8: Look for and express regularity in repeated reasoning

Subject Matter Texts and Exams: Level of Question (PISA) sense making

Page 20 – Chart 3

Findings sense making

Mathematics• Many community college programs demand little or no mathematics• Mathematics needed in many associate of applied science programs is mostly middle school mathematics• Students command of middle school mathematics concepts is weakRecommendations: Master middle school mathematics – Do notrush students through middle school mathematics Master Algebra I by sophomore year – make sure the emphasis is on using algebra as a tool in modeling and problem solving

Quoting the Report

Our sense making(NCEE) research shows that many of the most popular community college programs leading to well-paying careers require mathematics that is not now included in the mainstream high school mathematics program, including mathematical modeling (how to frame a real-world problem in mathematical terms), statistics, and probability.

Mathematical Sciences: 2025 sense making

The need to create a truly compelling menu of creatively taught lower-division courses in the mathematical sciences tailored to the needs of twenty-first century students in pressing, and partnerships with mathematics-intensive disciplines in designing such courses are eminently worth pursuing.

Page 10

Our research also shows that success in many sense makingcommunity college programs demands mastery of certain topics in mathematics that are rarely, if ever, taught in American elementary and secondary schools, including complex applications of measurement, geometric visualization and schematic diagrams.

Mathematical Sciences: 2025 sense making

It is not enough to rearrange existing courses to create alternative curricula; a redesigned offering of courses and majors is needed.

Page 11

Mathematics in Automotive Technology sense makingManufacturer’s specs state that pressure readings in drive should be within 10% of pressure readings in neutral. Is the drive reading as indicated below within spec? What are the possible explanations for this? What would be a possible customer complaint?

Infusing Mathematics into Automotive Technology Instruction

CORD and Michigan’s Dept. of Career Development

Math used in core courses

Math used in core courses sense making

Math used in core courses sense making

Math used in core courses sense making

Math used in core courses sense making

Discrepancy between the percent of text chapters containing mathematical content: mathematics courses vs program courses

Page 32 – Chart 14

Discrepancy between the percent of text chapters containing mathematical content: mathematics courses vs program courses

Page 33 – Chart 15

Discrepancy between the percent of exam questions containing mathematical content: mathematics courses vs program courses

Page 33 – Chart 15

Discrepancy between the percent of exam questions containing mathematical content: mathematics courses vs program courses

Page 33 – Chart 15

Findings mathematical content: mathematics courses vs program courses

Mathematics• Algebra II is not a prerequisite for success in community college or in most careersRecommendationHigh schools should abandon the requirement that all high school students take Algebra II.

Quoting the Report

Mastery mathematical content: mathematics courses vs program coursesof Algebra II is widely thought to be a prerequisite for success in college and careers.

The panel foundthis is not the case.

Requiring all H S students to take Algebra II may be an unnecessary barrier.

Mathematical Sciences: 2025 mathematical content: mathematics courses vs program courses

It is evident that, in view of the ever-increasing complexity of real life applications, the ability to effectively use mathematical modeling, simulation, control and optimization will be foundation for the technological and economic development of Europe and the world.

Page 84

Findings mathematical content: mathematics courses vs program courses

Mathematics• Mathematical modeling, statistics and probability, complex measurement, schematics and geometric visualization needed in many community college programs but not now taught in most schoolsRecommendationBroaden the scope of what is taught (required) in high school mathematics to include critical topics like statistics and probability (not simply as a separate course), mathematical modeling and other topics that strengthen the students’ ability to succeed in their career.

Quoting the Report

Findings mathematical content: mathematics courses vs program courses

Mathematics• Mathematics tested in community colleges falls far short of what is in students’ textbooks and short of what they need in careers they have chosen

Quoting the Report

What does this disconnect or bad alignment cost? mathematical content: mathematics courses vs program courses

Prerequisites required for College Algebra - based on percent of text chapters and exam items that utilize CCSSM domains

Page 70 – Chart G1

Fast percent of text chapters and exam items that utilize CCSSM domainsFacts (National Council of State Legislators)

- The need for remediation is widespread. When considering all first-time undergraduates, studies have found anywhere from 28 percent to 40 percent of students enroll in at least one remedial course. When looking at only community college students, several studies have found remediation rates surpassing 50 percent.
- Students are not testing at college-ready levels on national assessments. Only 25 percent of students who took the ACT met the test’s readiness benchmarks in all four subjects (English, reading, math and science) in 2012. A mere 5 percent of African Americans and 13 percent of Hispanics met the readiness benchmarks in all four subjects.
- Remediation is costly for states to provide and for students to take. Strong American Schools estimates the costs of remedial education to states and students at around $2.3 billion each year.
- Compounding the costs is the fact that remedial students are more likely to drop out of college without a degree. Less than 50 percent of remedial students complete their recommended remedial courses. Less than 25 percent of remedial students at community colleges earn a certificate or degree within eight years.
- Students in remedial reading or math have particularly dismal chances of success. A U.S. Department of Education study found that 58 percent of students who do not require remediation earn a bachelor’s degree, compared to only 17 percent of students enrolled in remedial reading and 27 percent of students enrolled in remedial math.

Prerequisites required for general mathematics courses - based on percent of text chapters and exam items that utilize CCSSM domains

Page 70 – Chart G2

Alignment based on percent of text chapters and exam items that utilize CCSSM domains– We (math departments) must do a better job at aligning what is required in our courses with what is required in majors. The old standards, Intermediate Algebra and College Algebra, like Algebra II in HS, are not appropriate for all students.

Promoting Mathematics based on percent of text chapters and exam items that utilize CCSSM domainsAcross the Disciplines – Evidence from texts suggest that mathematics can and should play a larger role in core courses – ‘we’ must help other faculty achieve that goal.

Depth based on percent of text chapters and exam items that utilize CCSSM domains – Too much emphases is placed on skills; in the core courses and often in mathematics courses. More prominence needs to be given to problems with which students need to grapple – struggle – reason about – problems in context.

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