[Students] need to develop a good number sense and the kind of familiarity with numbers that comes from use of paper and pencil techniques for acquiring skills in arithmetic.

By encouraging early and widespread use of technology in K-12 mathematics education, the Iowa Core undermines preparation for college-level mathematics.  As seen in Iowa Core: Mathematics, Part 1, students unprepared to succeed in college-level mathematics coursework will either see graduation delays as they spend time completing remedial mathematics work in college or will find themselves severely limited in their choice of majors.  For all the talk of needing more STEM majors, it is shame that the drafters of the Iowa Core failed to align the K-12 mathematics curriculum with the actual college preparation needs of students so clearly spelled out on the University of Iowa’s website.

One final note: although the Iowa Core Mathematics Curriculum is not aligned with University of Iowa expectations, it does seem to closely track the contents of the Core-Plus Mathematics Program (available here).

22M:001 Basic Algebra I

This developmental course covers what is usually taught in a first year high school algebra course. This course is often called Beginning Algebra or Intermediate Algebra at other schools. It does not carry credit towards graduation at Iowa. It begins with properties of the real numbers, covers algebraic expressions, products and factoring of algebraic expressions, exponents and radicals, linear equations/systems of linear equations and their graphs, and ends with quadratic equations, the quadratic formula, and graphing quadratic functions.

22M:002 Basic Algebra II

This developmental course covers what is usually taught in a second year high school algebra course. This course is often called College Algebra at other schools. It does not carry credit towards graduation at Iowa. Basic Algebra II covers algebraic expressions, products and factoring of algebraic expressions, fractional exponents and radicals, complex numbers, solving polynomial equations and inequalities, and functions including polynomial functions, rational functions, and exponential and logarithmic functions.

22M:003 Basic Geometry

This developmental course covers what is usually taught in a high school geometry course. It does not carry credit towards graduation at Iowa. It covers distance and angles, coordinates, area and volume, the Pythagorean Theorem, triangles, polygons, circles, solids, and vectors.

22M:005 Trigonometry

Trigonometry covers the six trigonometric functions, solutions of right and oblique triangles, vectors, and complex numbers.

22M:009 Elementary Functions

This is a standard one semester college precalculus course. It covers the same material as 22M:002 Basic Algebra II and 22M:005 Trigonometry, but is at a faster pace. It is not intended for students who have not seen trigonometry. Topics covered include functions, relations, coordinate systems, properties and graphs of algebraic, trigonometric, logarithmic and exponential functions, inverse trigonometric functions, and properties of lines and conic sections.

In addition to these course listings, the University of Iowa provides quizzes that cover important skills and concepts in arithmetic, algebra, analytic geometry, trigonometry, and logarithms and exponentials here.

Compare these listings to the Iowa Core Mathematics Curriculum Essential Skills and Content.  For example, the Iowa Core considers Statistics and Probability to be an essential mathematical strand (Core Math, p. 13) but I see no evidence on the University of Iowa website that Statistics and Probability are considered essential preparation for either Calculus or Statistics at the college level.  Under the Geometry strand, the Iowa Core lists vertex-edge graphs as an essential topic (Core Math, p. 42).

Students should understand, analyze, and apply vertex-edge graphs to model and solve problems related to paths, circuits, networks, and relationships among a finite number of elements, in real-world and abstract settings. Important vertex-edge graph topics for the high school curriculum include: Euler and Hamilton paths and circuits, the traveling salesman problem (TSP), minimum spanning trees, critical paths, shortest paths, and vertex coloring.  (Core Math, p. 44-45).

Again, I see no evidence on the University of Iowa website that studying vertex-edge graphs is essential preparation for either Calculus or Statistics at the college level.

It strikes me that the drafters missed the mark in determining essential skills and concepts in at least two ways.  First, if parents, teachers, and school districts need a consistent description of Algebra I and Algebra II topics*, the Iowa Core has not provided one; the Iowa Core does not provide any guidance about dividing algebra topics into Algebra I and Algebra II courses.  Second, by failing to acknowledge college-level mathematics as an endpoint for many of Iowa’s K-12 students, the drafters of the Iowa Core have cluttered the standards with non-essential topics.  The drafters could have created a K-8 sequence of math topics that would align with and prepare students for a college-preparation mathematics sequence in high school.  Instead, they have created standards that may be mathematically interesting but do not focus on college-preparation.  There is no evidence that Iowa students have so effortlessly mastered college-preparation mathematics topics that they can afford the distraction of non-essential topics, nor is there evidence that the University of Iowa mathematics department has made a mistake in describing major mathematics topics that students need to have mastered to prepare for success in college-level mathematics course work.

*In other words, do the course titles “Algebra I” and “Algebra II” at any particular school represent coverage of authentic Algebra I and Algebra II topics or do they represent, for example, Algebra I topics spread out over two years.  Inconsistent course-labeling could lead to problems for students changing schools.  It also creates problems for parents and students trying to determine whether a student is actually taking a college-preparation math sequence.  Do the course titles “Algebra I” and “Algebra II” provide coverage of the topics that the University of Iowa expects to have been covered when requiring completion of those courses for college admission?

• Teaching for Understanding

• Problem-Based Instructional Tasks

• Distributed Practice that is Meaningful and Purposeful

• Mathematical Modeling (secondary school emphasis)

• Deep Conceptual and Procedural Knowledge

• Rigor and Relevance

• Effective Use of Technology

• Connected and Coherent Content

Conspicuously absent is any mention of college preparation.  (Note that any mention of ensuring mastery of the material is also missing from the list).  Should a “world-class mathematics curriculum” prepare students for college level mathematics coursework?  I think the answer is obvious.  Does the Iowa Core Mathematics Curriculum focus on mathematics topics that will prepare students for college level mathematics coursework?  One way to begin to answer this question is to examine what the University of Iowa has to say about preparation for college math:

Many college majors require math beyond what you learn in high school.  To make good progress in college, you need to be ready for the recommended first course in your major.  Being ready in math is also an important part of being ready in science, engineering, nursing, computer science, and statistics, or even in the economics you’ll need for business. Math matters in lots of majors.

The following majors require students to be prepared to start with 22M:25 Calculus I or 22M:31 Engineering Math 1: Single Variable Calculus.  These courses require mastery of the work in first year algebra, second year algebra, trigonometry, and pre-calculus.

• Actuarial Science B.S.
• Astronomy B.A. or B.S.
• Biochemistry B.A. or B.S.
• Biomedical Engineering
• Chemical and Biochemical Engineering B.S.E.
• Chemistry B.A. or B.S.
• Civil and Environmental Engineering B.S.E.
• Computer Science B.A. or B.S.
• Economics B.S.
• Electrical and Computer Engineering B.S.E.
• Environmental Science B.S.
• Geoscience B.S.
• Industrial Engineering B.S.E.
• Mathematics B.A. or B.S.
• Mechanical Engineering B.S.E.
• Physics B.A. or B.S.
• Sociology B.S.

The following majors require students to be prepared to start with an applied calculus course (22M:17 Calculus and Matrix for Business; 22M:16 Calculus for the Biological Sciences).  These courses require mastery of the work in first year algebra, second year algebra, and pre-calculus.

• Accounting B.B.A.
• Biology B.A. or B.S.
• Economics B.B.A.
• Finance B.B.A.
• Informatics B.A. or B.S.
• Integrative Physiology (Exercise Science) B.S.
• Management B.B.A.
• Management Information Systems B.B.A.
• Marketing B.B.A.
• Microbiology B.S.
• Political Science B.A. or B.S.
• Psychology B.S.

The following majors require students to be prepared to start with 22M:15 Math for Biological Sciences.  This course requires mastery of the work in first year algebra and second year algebra.

• Clinical Laboratory Sciences B.S,
• Geography B.S.
• Radiation Sciences B.S.
• Speech and Hearing Science B.A.

The following majors require students to be prepared to start with an applied statistics course (22S:25 Elementary Statistics and Inference).  This course requires mastery of the work in first year algebra and second year algebra.

• Athletic Training B.S.
• Geography B.A.
• Health and Sport Studies B.A.
• Leisure Studies: Therapeutic Recreation B.S.
• Nursing B.S.N.
• Psychology B.A.

The following majors require students to be prepared to start with 22M:9 Elementary Functions.  This course requires mastery of the work in first year algebra, second year algebra, and trigonometry.

• Nuclear Medicine Technology B.S.
• Sociology B.A.

The following majors require students to be prepared to start with 22M:6 Logic of Arithmetic or 22M: Theory of Arithmetic.  Logic of Arithmetic requires mastery of the work in first year algebra.  Theory of Arithmetic requires mastery of the work in first year algebra, second year algebra, and pre-calculus.

• Elementary Education B.A. or B.S.

The following majors require no specific mathematics or statistics courses.

• African American Studies B.A.
• American Studies B.A.
• Ancient Civilization B.A.
• Anthropology B.A.
• Art B.A. or B.F.A.
• Art History B.A.
• Asian Languages and Literature B.A.
• Cinema B.A.
• Classical Languages B.A.
• Communications Studies B.A.
• Comparative Literature B.A.
• Dance B.A. or B.F.A.
• English B.A.
• French B.A.
• German B.A.
• History B.A.
• International Studies B.A.
• Italian B.A.
• Journalism and Mass Communications B.A.
• Linguistics B.A.
• Music B.A. or B.M.
• Philosophy B.A.
• Portuguese B.A.
• Religious Studies B.A.
• Russian B.A.
• Social Work B.A.
• Spanish B.A.
• Theatre Arts B.A.
• Women Studies B.A.

In Rent Seek and You Will Find, Duke Professor Michael Munger discusses the problem of city governments competing for federal grants.  This problem also applies to states seeking federal grants, as in the Race to the Top program.

[Y]ou have to pay for free money twice: first you have to collect the money, out of tax revenues. And then you have to pay for the money again, because the benefits are dissipated by what economists call “rent-seeking.” Let me explain.

The technical definition of rent is any return to investment, or effort, that exceeds the opportunity cost rate of return. So, Alex Rodriguez of the New York Yankees earns a large rent, or premium, because of his scarce talents as a baseball player. He could earn a living as a banker, or a waiter, or something else. But it is unlikely that he could earn anything close to the $25 million per year he makes as a baseball player. Those rents encourage competition. And in most economic situations, that competition for profits produces benefits. But in politics, competition for those rents is often destructive.

The greater the rent, the greater the costs people are willing to incur to win it. When government hands out what appears to be free money, people are going to scramble to get some of it, incurring costs as long as those costs raise the chances of winning the “free” money sufficiently.

Unfortunately, in Iowa the costs of competing for Race to the Top funds are not easily seen.  How many dollars have been spent on consultants?  How many dollars have been spent on public employees to draft legislation, draft two rounds of Race to the Top applications, and now to align the CCSSI to the Iowa Core?  What opportunities have been lost to pursue other avenues of school reform that might actually raise student achievement instead of committing ourselves to the ones that are favored by the current Washington D.C. political elite?  How many hours and how many dollars already dedicated to implementing the Iowa Core will have been wasted as we scramble to adopt a new set of standards, even as we have already lost out on the funding they were supposed to help us win?  Are the costs incurred less than the amount we had hoped to win, which would have been at best, less than 1% of the current K-12 education budget (and is in fact, now, zero)?  Professor Munger continues:

[S]pending city money to win pretty much the same amount of federal money makes little sense economically. But it makes a lot of sense politically. As long as politicians are able to claim credit for bringing new federal spending to their state, district, or city, it doesn’t matter that each dollar “won” actually cost 30 cents, or even $1.20.

Remember that, as Senate Republican Leader Paul McKinley attacks the Democrats for not doing more to pursue Race to the Top funding:

It should come as no surprise that Iowa was not selected as a finalist for the national “Race to the Top” grant program considering Governor Culver and legislative Democrats submitted an application that failed to meet the essential guidelines laid out by the Obama Administration. Senate Republicans attempted to improve Iowa’s chances by advancing key areas regarding pay for performance, student achievement and charter schools among others but Culver and his allies chose to listen to their union bosses and instead ignore the needs of our students.

Would our students be served by a pay for performance program?  How would one even work?  Are there any school districts successfully using a pay for performance plan to boost student achievement?  Would designing and implementing a pay for performance plan cost more than the Race to the Top grant award Iowa might have won?  Who cares when there is federal money on the table?  Arguably, the only potential winners here are the politicians.

Update: The Iowa Board of Education has adopted the Common Core State Standards.

Hat tip: Division of Labour.

All this means dramatic change for our schools and our curriculum – both in content and in delivery styles. (p. 8 )

What is the evidence provided in the Model Core, if any, that supports the assertion that the Iowa legislature should have mandated any dramatic change in the content and delivery styles of the school curriculum?*  What is the evidence provided that the Iowa legislature should have mandated the particular changes described in the Iowa Core documents?  As we examine these questions, please consider Jay P. Greene’s observations on the problems of relying upon expert panels (read the whole post here):

The experts do not necessarily represent all or the best views on the matter and may simply be selected by the researchers for their predisposition to support the researcher’s favored conclusion.  In other words, we don’t learn anything from these analyses.  It is simply a way of disguising and making more impressive the opinion of the researchers for the purpose of political manipulation.

Anyone interested in serious education research should shun professional judgment studies, whether for spending adequacy or for education standards.

While Professor Greene is not describing the drafting of standards, the Iowa Core was drafted by an “expert panel” selected by the Iowa Department of Education, as examined in Part 1.  Is there evidence in the introductory material that these team members represented or reviewed all or the best views in education reform and standards?  The Model Core appears to rely heavily upon the works of Professor Chris Dede (Harvard University) and Dr. Willard Daggett (International Center for Leadership in Education).  (p.12)  However, the amount of reliance on these two sources (or any other sources) is unclear because the drafters failed to use internal citations.  (Also missing is any explanation of how or why these two particular sources were singled out of all possible education experts to shape the Iowa Core.)  Thus, when the drafters make the following assertion that Iowa schools must undergo a dramatic change, there is no reference to any authoritative evidence that any of these reasons for change in fact exist outside the consensus of the team members.

The international economy and the U.S. job market aren’t the only significant areas of change.  Students have changed, too.  Today’s high schooler is a product of the Net Generation, a life of iPods, instant messaging, cell phones, Xbox games, and Google. Multi-tasking is a given. But those changes don’t always extend to learning and teaching styles.  Too many students tune out once inside the classroom.  Dropouts include some of our best and brightest who simply aren’t engaged by the same old teaching styles. Schools that successfully captivate this information-age mindset with higher-level learning find student motivation explodes, and not just among the top performers.

The message then is clear: Students shouldn’t be expected to power down at the schoolhouse door.

All this means dramatic change for our schools and our curriculum – both in content and in delivery styles. (p.8)

There is no evidence provided that multi-tasking should be a given or that the problems in education are due to students tuning out (as opposed to text book selections, full-inclusion classrooms, class-size, or teacher quality, for example).  There is no evidence provided that the best and brightest “simply aren’t engaged by the same old teaching styles,” nor is there any research cited that proves that student motivation will explode if schools “captivate this information-age mindset with higher-level learning,” however that is supposed to be done.  Professor Dede’s new learning styles are described a few pages later and suggest how the team members believe that students should be captivated in schools.

In a videoconference with the Lead Team, Dr. Dede shared his passion for changing teaching styles to reach the tech-savvy student.  He reviewed cutting-edge efforts to apply a video-game-like learning environment to deliver higher-level, complex learning.  Rather than listen to a lecture on the environment, for example, students might use a handheld computer and enter a virtual reality world where real-time problems arise and students must develop solutions on the fly.

These learning styles produce successful, motivated students.  Even lower-performing students get fired up when they realize they can combine a love for technology and video-gaming with higher-level learning. (p. 12)

Think about that.  The team members are endorsing the idea that schools should be transformed into a place where video games replace teacher-led instruction without any citations to research that supports the idea that this is the best or only way to motivate student learning, let alone to actually have students learn anything.  In an interview with Innovate, Professor Dede explains how he sees this working.

Steinkuehler (2004) has done preliminary research on the forms of cognition generated within multiplayer online games. Her findings support the idea that, armed with sophisticated instructional design, we can embed learning activities in graphically rich virtual worlds. For example, we could have young students encounter ethical dilemmas that increase in complexity as they advance through a Narnia MUVE [multiuser virtual environment], which would be based on the stories of C. S. Lewis. Older students could participate in a Star Trek MUVE (Dede and Palombo 2004) that integrates mathematics as they navigate the Starship Enterprise, engineering as they maintain the warp engines, and anthropology as they learn to communicate with alien species.

This sounds thrilling, for the sort of student who might want to spend time playing a Star Trek navigation game anyway.  But what disciplines can really be presented well in this manner?  Do students need to spend time learning to communicate with alien species or could they use more time to read grade-level texts and practice writing skills? Is this the most efficient way to deliver content and opportunities for practice?  Is it possible that instead of trying to motivate students through video games that students would be better served by schools that teach them scholarly habits.  For example, Montessori activities are designed to help children to develop longer periods of concentration, and the teachers encourage the children to learn to carefully attend to details, to complete their work, and to work without disturbing others.  What is the evidence that instead of instilling good habits from the earliest grades we should just try to entertain students?

The other apparent major source used to shape the Iowa Core is Dr. Daggett, who is credited with the rigor and relevance quadrant framework that is used throughout the Iowa Core documents.  (Dangerously Irrelevant has a post on Dr. Daggett here.)

To recap, the premise of rigor and relevance says high schools can no longer get by teaching a set of facts. Instead, they must also teach students how to think and how to apply those facts in problem-solving situations that eventually involve real-world situations. “Stretch learning” is another term for this teaching approach.

The benefit is a high school graduate armed with a deeper understanding of a given subject and, more important, an appreciation for how the facts that may still be learned by rote will be relevant to his or her future. (p. 12)

There is no evidence provided that Iowa high schools have been only teaching facts.  Nor is there evidence provided that real-world problems are superior to other methods for teaching students content or how to think.  The suggestion that teaching students how to think is a new innovation is absurd.  The Socratic method, logic, rhetoric, and geometrical proofs, for example, all pertain to teaching students how to think.  There is no evidence provided for the assertion that “stretch learning” arms students with a deeper understanding of content and an appreciation for facts.  Consider also the implicit claim that the drafters of the Iowa Core can predict with certainty what will or will not be relevant to any particular student’s future.  How can they possibly know?

It is incumbent on the Iowa Core supporters, as proponents of dramatic change, to demonstrate that these particular recommendations are supported by evidence.  Without internal citations, it is difficult to read the Model Core as a serious, objective attempt to review all or even the best of thinking on education reform or the best of education research.

*Keep in mind that Iowa is a state of very little educational choice.  Each school district and accredited non-public school is required to implement the Iowa Core.

Hat tip: kitchen table math.

A Lead Team – representing teachers, students, administrators, school board members, higher education, the business community, and experts in the fields of science, literacy, and math – laid the foundation for what is included here. (p. 4)

The lead team members are listed on page two.  Note that the members are listed by affiliation but without credentials.  That is, there is no basis for determining that any of the team members are experts in the fields of science, literacy, and math by the information provided in the report unless “expert” means being an employee at the Department, an AEA, a school district, or a college.  There is a PhD in math education but I could not easily confirm through an internet search that any of the lead team members holds a PhD in any of the disciplines listed.

Lead Team members suggested members for all three [work teams], and the Department of Education also identified candidates. In the end, Work Team membership included experts from the content areas and various levels of education: higher education, both two-year and four-year programs; high school, K-8, and area education agencies. (p. 14)

The work team members are also listed on page two, and again there is no information provided to indicate what might qualify the team members as experts.  The science team has three consultants, two high school teachers, two science education PhDs, and a community college instructor.  Among them, one is a chemistry teacher, two are in biological sciences and one in physics.  I could not easily determine the areas of interest for the other four team members.  The literacy team has four consultants, one library media specialist, one teacher/librarian, one teacher, two curriculum specialists and one community college professor holding an MA in teaching.  The math team has five consultants, three teachers, and three college instructors (one of whom holds a PhD in math and one with a PhD in math education).

Of particular interest is the PhD in math education who also happens to be a co-author of the Core-Plus textbook series.  Some links to information critical of Core-Plus is available NYC Hold.  It is troubling that his relationship to this math textbook series was not disclosed, not only because of his own potential self-interest, but also because the Department appears to have steered the Model Core Curriculum into favoring reform math without being straight-forward about their efforts.  Indeed, it is possible that a parent or legislator with no knowledge of the math wars or constructivism would have no idea how controversial these standards might be; the words math wars, reform math and constructivist/constructivism appear nowhere in this document.

The Iowa Core Curriculum consists of (at least) seven documents numbering over 500 pages: the Model Core Curriculum, K-12 Literacy, K-12 Mathematics, K-12 Science, K-12 Social Studies, 21st Century Skills, and Birth to Five.  The Model Core Curriculum is available for download here.   Birth to Five is available for download here.   The other documents are available at the Iowa Core website.  [Note:  I am using downloaded versions dated January 2009 and July 2009.  Changes may have been made since I downloaded these documents.]

Some questions to consider:

Who wrote these documents?

What content and skills were chosen?  Do they reflect content and skills of enduring value or more ephemeral in nature?  Do they build a strong foundation for college-level work without remediation?  Do they reflect college admissions requirements?  Do they reflect developmentally appropriate expectations?  That is, are children being expected master foundational, basic skills or are they expected to behave as experts?  What are the opportunity costs?

How are the content and skills to be taught?  Are the methods efficient in the use of classroom time, student time outside of class, money, and resources?  Are the methods effective in helping students learn the content and develop their skills?  What are the opportunity costs?  How will we know if students have acquired the content knowledge and skills?

Why these particular changes?  What is the evidence that integrating content rather than using more traditional subject disciplines is necessary or desirable?  What is the evidence that these methods will result in higher student achievement than more traditional methods?

I hope to work my way through all of the documents (again), starting with the Model Core Curriculum.

In the Iowa Core Curriculum K-12 Literacy Essential Concepts and Skills document, the word handwriting appears twice.  Two times in 130 pages.

From the Iowa Core, primary level (K-2):

Essential Concept and/or Skill: Write on demand.

• Consider audience and purpose

• Focus on a single topic

• Draw upon experiences and observations

• Use correct spelling of high-frequency and grade-level words

• Create readable documents with legible handwriting

Legible handwriting is not even mentioned for grades 3-12, let alone as a stand-alone essential skill at any grade level.  Why does this matter?  First, as ktm commenter palisadesk notes, if it isn’t in the curriculum, it won’t be taught.  Second, being able to write quickly and legibly is an important skill.  One that is necessary for taking notes, especially in math and science, but also needed for constructed response exams and ACT/SAT essays, as well as college blue book exams.  Legible handwriting requires plenty of practice so that it can be done automatically and without tiring out the child’s hand.