New Jersey Coalition for World Class Math

These are the current New Jersey Core Curriculum Content Standards for Mathematics 

June 3, 2009 Joint Committee on the Public Schools

On June 3, 2009, several members of our Coalition presented publuc testimony at the Joint Committee on the Public Schools.  The main thrust of our tesimony was that there are no proper documented written processes and procedures for the writing, reviewing, and revising of core curriculum standards.  Everyone of our coalition members (parents and professors) and special guests, Dr. Stotsky and Dr. Dancis, who spoke did an absolutely amazing job!  Thank you all so much!

 February 2009 UPDATE!!! 

The NJDOE is moving towards world class standards which are aligned to many of our coalition's philosophies.  They have made changes to their first two drafts.  See the Feb. 4, 2009 Math Standards Draft Here:

Math_standards_for_posting_02_04_09_with_intro.doc

Just added... Read comments on the February Revisions Draft from several math professors (PhD's in Mathemathatics) from across the nation, two of whom were on the National Mathematics Advisory Panel, Dr. Wu (University of California at Berkeley) and Dr. Fristedt (University of Minnesota.

Comments.Prof.Wu_Prof. Bechtold_Prof. Fristedt.doc

Comments.Prof. Raimi_Prof. Milgram_Prof. Bisk.doc

Comments.Prof. Dancis.doc

Mercer County Community College's Department of Mathematics Chair, Professor Edith Silver, Professor Yvonne A. Greenbaun, and Professor Nicholas N. Greenbaun, have written a commentary on the NJ Math Standards and have sent it to the NJDOE.

The draft standards are getting closer, but are still not yet world class and internationally benchmarked.   Input will continue to be sought from the Coalition’s advisory panel of mathematicians and their feedback will be provided to the NJ DOE. 

Send us your opinion of the new draft by the end of March and we will forward to the NJDOE.NJWorldClassMath@Yahoo.com

Or see the draft on their web site: http://www.nj.gov/education/aps/cccs/2009/math/index.html 

On the above link, be sure to review that Draft of Algebra 1 Core Content and see the 2009 Revised Standards Evaluation Tool

NEW! IMPORTANT! Read the memo from the NJDOE urging district superintendents not to buy new materials based on the current 2004 standards since they will be replaced this year.  They also urge districts not to use the current draft to revise their curriculum.  See the entire memo: njdoememo3.9.09.pdf 

 Read the Public Testimony of some of our coalition members which was presented to the State BOE at the January 21, 2009 NJBOE meeting: NJBOE Public Testimony.1.21.09.doc

December 2008 UPDATE!!!

There is now a 12/2/08 Draft.  There is still no mention of the Standard Algorithm, there is still calculator use in 2nd grade, it is still in a format that is not coherent, focused or user-friendly, and it does not in any way resemble World Class Math Standards.

Here's the Draft: math_PreK_HS_complete_12_02_08_.doc

After several requests, the NJDOE sent one of our members the names of who participated on the Standards Writing Team: Math_Team_Historical_for_Release_Jan_08_2009.doc

   November 2008 Important Announcement!!

The New Jersey Department of Education is nearing completion of Revised Math Standards!!  They may be adopted by the State BOE in early 2009. 

See the 10/16//08 draft of revisions here: math_PreK_HS_horizontal_10_16_08_withoutestimation.doc (they are not posted on the NJDOE web site)

This is our opportunity to ensure that the New Jersey Department of Education writes and provides world class math standards!!!

Does the October 16, 2008 revised math standards draft meet "world class" standards?  Absolutely not!

Leading mathematicians, as well as concerned citizens, agree.

See Criticism of NJ's Revisions  (all forwarded to the NJDOE)

Just added math professors' comments on Feb. 2009 Draft: 

Comments.Prof.Wu_Prof. Bechtold_Prof. Fristedt.doc

Comments.Prof. Raimi_Prof. Milgram_Prof. Bisk.doc

Comments.Prof. Dancis.doc

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Comments on the 10/16/08 NJ Math Standards Draft From Leading Experts in the Field of Mathematics (all were forwarded to the NJDOE after review of the 10/16/08 NJ Math Standards Draft and the Dec. Draft was not too different)

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I have looked over the new Draft New Jersey Mathematics Standards and am quite discouraged by them.  They do not meet even minimal standards.

For example, the First Number standard "Numbers are used for counting, ordering, comparing and labeling objects in the physical world" focuses strictly on the USE of numbers as counting objects, not on what numbers are (sets with two operations, + and times, that contain 0, 1, satisfy the associative and commutative laws for both operations and the distributive law between them, and so that both operations satisfy appropriate cancellation laws - for example a + b = a + c if and only if b = c.)  In the programs in the high achieving countries, it is assumed students coming into first grade can count, but they regard it is the main job of the schools to teach children what numbers really are.  Oddly enough, the students in those programs have very little trouble with fractions as well as ratios and proportions when they come to them, whereas it is exactly at this point that most of our students become lost.

Of course, this misconception is more or less the norm throughtout the United States,  It is just more blatant in the New Jersey Draft Standards.

But leaving that aside, there are also blatant errors such as the seventh grade standard:
"Understand that all fractions can be represented as repeating or terminating decimals."
There is a world of difference between "ultimately repeating decimals" and "repeating decimals," and it's a sad commentary on the likely math competence of the writers who were not careful about this distinction or did not understand it.

And it is hard to imagine anything more empty of intellectual content that the major standard, "Logical patterns exist and are a regular occurrence in mathematics and can be described using mathematical language."  What can this possibly mean?  What is a "logical pattern?" For that matter, what is a "pattern?"  I thought I knew what the word was meant to signify in state standards and other math education documents, but that meaning had no possible attachment to the word "logical."  So I am completely confused.

Overall, I am fully in agreement with the comments of Prof. S. Wilson whose extremely critical remarks were recently sent to you.  These standards need a huge amount of work by people far more aware of the key issues and what basic notions students have to understand in order to have a chance to become mathematically knowledgeable.

Far more attention needs to be paid to the NCTM Curriculum Focal Points, and the recent report of the National Math Panel.  A few forward looking states are restructuring their frameworks so that they precisely align with these two basic documents.

Yours,
R. James Milgram

R. James Milgram, Professor of Mathematics, Stanford University

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First, the table of contents probably says enough, but we can always be surprised.  When you see major headings that include "Patterns", (4.3 Patterns and  Algebra), it is time to get suspicious.  Likewise when you see 4.4.   Data Analysis, Probability, and Discrete Mathematics, and 4.5.   Mathematical Processes.  The odds are already against having decent  standards, and that is only the table of contents. 

Next, consider the formatting of the document.  A mind orderly enough to created decent standards could not invent that formatting.  Strike 2, but they still have a chance.

Gack, a little variation please.  First thing you see, 4.1.P A. Number Sense, PreK Content, Numbers are used for counting, ordering, comparing and labeling objects in the physical world.  Follow this  through until 4.1.12 A. Number Sense Grade 12 Content, Numbers are  used for counting, ordering, comparing and labeling objects in the  physical world.  Well, at least they are consistent.

I was about to quit and say the innards don't look so bad when I got to Grade 5 CPIs, 2.  Construct, use, and explain procedures (pencil-and-paper or mental math) for performing addition and subtraction with fractions and decimals. [The problem here is "construct".  How do you construct a definition?]

Grade 5 CPIs, 4 "Select and apply the appropriate method of computation from among pencil-and-paper, mental math, and use of a  calculator or computer to solve real world problems. [How many fuzzy math jargon phrases can you put in one sentence without even trying?]

Grade 5 CPIs, 5 "Add or subtract fractions and decimals using estimation strategies."  [Okay, I give up.  What does that mean?] 

Grade 5 4.3.5 A. Patterns  "Algebra provides language through which we  communicate the patterns in mathematics."   [Who do they go to to make up phrases like this?  It would be a great social studies project to track down where this came from.  I doubt if it came from anyone 
who knew mathematics well, and if it did, it was misunderstood and turned into a cornerstone of K-12 math education.  Why aren't people who know mathematics taken seriously when it comes to mathematics education?]

Grade 5 CPIs 1 "Recognize, describe, extend, and create patterns involving whole numbers.” If you are reading standards and you see a sentence with 3 of the 4 words in "Recognize, describe, extend, and create" then you know the standards are corrupted.  [It doesn't even have to be followed by "patterns", which makes it all too obvious for words.]

4.3.5 B. Grade 5 CPI 1 "Describe arithmetic operations as functions, including combining operations and reversing them."  [Right, functions of 2 variables.  Just what I'm teaching right now.  We call it  Calculus 3.  Try using grade appropriate language.]

4.3.5 C?  Procedures.  Grade 5 CPIs "Solve two-step linear equations  with manipulatives and informally (e.g. working backwards)."  [Seems  like if they are using manipulatives to solve algebra equations they  are already doing things backwards.]

I'm normally inclined to skip the data/prob/stat sections in standards, but this one caught my eye, still Grade 5 "Estimate and determine probability using intuitive, experimental, and theoretical methods."   [I've heard of experimental and theoretical methods, but it appears that "intuitive methods" have replaced "computational  methods", which I had also heard of.  I hadn't heard of "intuitive methods".  I do wonder how this is tested, with a Ouija board?] 

I was going to take a look at grade 9 on the assumption it might be algebra, but there is grade 8 and then it skips to grade 12. One just caught my eye for grade 12:  "Develop, apply and explain methods for solving problems involving rational and negative exponents.  [Such as] "laws of exponents"  [come on, give me a break.  Do we need to develop the law of exponents?]
 

You can't make this stuff up!  4.3.4 A. Patterns  Grade 4  Content, but actually it looks like this is the same for all grades,  and well it should be.  "Logical patterns exist and are a regular occurrence in mathematics and can be described using mathematical language."  [Sorry, got to put that one with my collection of all time great quotes.]

No "complete the square" for quadratics.  Things start getting vague (fuzzy?) higher up.

Okay, I obviously didn't read everything and just pointed out a few pitfalls along the way that I did see.  The language of the standards is reform.  If the standards are judged to be any good, it will have to be despite the reform language.  It is not likely that they can be all that good if the reform language is so strong.  I particularly point out the phrase "recognize, describe, extend, and create patterns" as a dead give away.

We were asked not to just throw stones but to give constructive criticism.  Every line needs tweaking.  If they promise to accept all tweaks, I'll tweak, but I sure won't just rewrite the standards line by line knowing that it will be completely ignored.  Tell them to have a panel of 3 research mathematicians who regularly teach engineers go  over the standards for them.  Mathematics education should ultimately be about the math, but that could just be the narrow minded mathematician in me leaking out.  The standards should make mathematical sense.

W Stephen Wilson
Professor of Mathematics
Department of Mathematics
Johns Hopkins University
Baltimore, MD 21218               wsw@math.jhu.edu

http://www.math.jhu.edu/~wsw/

Former Senior Advisor for Mathematics
Office of Elementary and Secondary Education
United States Department of Education

   ---------------------------------------------------------------------------- 

After looking at your new draft math standards they remind me a lot of the standards we just got rid of in Washington State.  Others have commented on some of the technical issues in the standards so I will just comment in general.  

The first question I would ask is who are math standards for?  If they are not primarily for teachers to use then they have very little value at all. The old Washington standards were so vague that they did not provide specific targets for teachers to aim at. The result was that teachers largely ignored the standards because they were irrelevant to what they did.  Your draft standards seem to have many of the same problems.  The question you need to ask about a standard is will Teacher A teach the same content as Teacher B when using the standards as their guideline. When looking at your standards, I would say the answer to that question is “very unlikely”.  If standards don’t direct teachers to the same target then they are not standards at all.

Secondly, the strand format is not created to help teachers. This format may be okay for curriculum directors to see the overall picture of how mathematics is tied together over the grades, but it does very little to help teachers in each specific grade. A 5^th grade teacher wants to see what students are expected to learn in the 5^th grade.  If they have to look through many strands to figure that out they simply won’t do it. Standards are hard enough to use without making them cryptic on top of it.  The format of your standards is not user friendly and that means they simply won’t be used by teachers in any meaningful way.

Simpler is better. It is obvious whoever wrote your draft standards leans towards reform. Standards should be pedagogically neutral. They should not suggest how students should learn but what they should learn. Standards that suggest leaning in context are pedagogical not a descriptive of what a student should learn. Some of your standards fall into that category.

The best standards to model as far as clarity are either the California or Indiana standards. These standards, though not perfect, are written in a way that leaves little doubt about what a teacher should teach or what will be assessed on a state test. Standards that do not provide these specific targets will only lead to poor performance in the classroom and on statewide tests.

You can see the comments I gave on the Washington standards at a recent University of Washington forum on Youtube. They can be found here: Standards 1  and Standards 2.

Best of luck,

Bob Dean

Bob Dean, Washington State Board of Education Math Advisory Panel & OSPI Standards Revision Team 

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These make you want to cry.  They have the look and feel of the old WA Math Standards.

Consider….Grade 3

4.1.3 A.  Number Sense

Grade 3 Content

1. Read, write, interpret, and use numbers in a variety of contexts.

•             Whole numbers through ten thousands  (<= 99,999)

•             Commonly used fractions (denominators of 2, 3, 4, 5, 6, 8, 10) as part of a whole, as a subset of a set, and as a location on a number line, including values greater than 1

2.  Demonstrate an understanding of whole number place value concepts through ten thousands.

3.  Explore the extension of the place value system to decimals through hundredths.

4. Compare and order whole numbers through ten thousands and demonstrate a sense of the relative magnitudes of numbers.

[5.   Understand the various uses of numbers.

•             Counting, measuring, labeling (e.g., numbers on baseball uniforms), locating (e.g., Room 235 is on the second floor)]

5. Compare quantities without counting

6. Identify whether any whole number is odd or even.

7.  Count and perform simple computations with money.

•             Cents notation (¢)

•             Dollars (without cents)

8. Construct and use a variety of estimation strategies (e.g., comparing to benchmarks) for estimating quantities.

All the vagueness of the old WASL standards.  How will different teachers know what to teach and testers what to test?  Very sad.

You should look at the WEMS (Washington Math Standards) posted online.

From,

David A. Orbits

Computer Design Engineer
Masters Degree in Computer Engineering, University of Michigan

David Orbits' Reviews of Washington State's First and Second Math Revisions Drafts:

WA_DEC_2007_Draft_Math_Standard_Comments.pdf

 WAJAN2008REFCOPYSENTOUT.pdf

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Sent to Dr. Robert Riehs of the NJDOE 11/10/08

Dear Bob,

Sent 1//10/08

Overall:

There are too many topics.  I would like to see less topics covered and the standards to promote mastery.  I would like the standards to specify which algorithms much be mastered for addition, subtraction, multiplication and division. I would like to see the function machines and input and output tables removed.  I would insist that the algorithm of choice be the traditional method.  Other countries expect so much more of their children.  The overall bar on these requirements needs to be raised in order for our children to be competitive globally.

I am concerned that the math standards do not map directly to the high school mathematics courses.  We go from grade 8 to grade 12.

I would like to a layout that is easy to follow which actual problems that demonstrate the standard.  You may want to look at the California State Math Standards.  They are easy to follow and implement.

1^st Grade:

·         Mastery of the addition and subtraction facts to 20.  I would like to see basic word problems that can be solved with addition or subtraction with the math facts.

·         Apply the meaning of addition and subtraction through appropriate words like putting together, increasing, taking away, comparing and finding the difference.

·         Solve addition and subtraction problems with one and two digit numbers.

·         Find the sum of three one digit numbers.

 2^nd Grade:

Addition and subtraction of 2 and 3 digit numbers and the associated word problems.

 3^rd Grade:

Move mastery of multiplication and division facts from Grade 4 to Grade 3.

• Understand place value to the 10,000s place. Count, read and write numbers to the 10,000s place.  Compare and order whole numbers to 10,000.
• Solve word problems with sum and difference.
• Addition and subtraction of 3 and 4 digit numbers.
• Introduce two step word problems.
• Solve word problems that applies the basic multiplication and division facts.
• Multiply a 3 digit number by 1 digit number.
• Division with a remainder
• Division of a 2 digit number by a 1 digit number
• Division of a 3 digit number by a 1 digit number
• Add and subtract dollars and cents.
• Addition and subtraction of hours and minutes (time).
• Addition and subtraction of simple fractions.
• Understand that decimals and fractions are two representations of the same number.
• Be able to translate a mathematical relationship expressed in words to a number sentence.
• Be able to do simple unit conversions like inches to feet and vice versa or yards to feet and vice versa.
• Carry out simple unit conversions with a system of measurement (e.g., centimeters and meters, hours and minutes)
• Determine unit cost when given the total cost and number of units.
• The ability to solve two-step word problems.
• Identify, describe and classify polygons (including pentagons, hexagons and octagons)
• Identify attributes of triangles (isosceles, equilateral, right triangle)

 4^th Grade:

Read and write numbers in the millions

• Reinforcement of multiplication and division by a 1 digit number
• Multiplication of a 2 digit number
• Understand and apply multiples and factors
  • Prime factorization of small whole numbers.
• Add and subtract fractions with a common denominator
• Add and subtract fractions with different denominators.  This requires the ability to use multiples (least common denominator)
• Solve simple fraction word problems.
• Understand mixed numbers
• Ability to convert from a mixed number to an improper fraction and vice versa.
• Ability to write a fraction in simplest form.
• Ability to find equivalent fractions.
• Solve problems with fraction of a set.
• Area and perimeter of composite figures.
• Understand decimals to thousandths.
• Express decimals as fractions
• Ability to express fractions with denominators of 4, 20, 25, 2, 5 and 50 as a decimal.
• Order and compare decimals.
• Rounding decimals.
• Be able to place decimals and fractions on a number line.
• Be able to compare fractions or decimals with equalities or inequalities.
• Master the four operations of decimals: addition, subtraction, multiplication and division with the traditional method.
  • Multiply a whole number by a decimal number.
  • Divide a decimal number by a whole number.
  • Solve appropriate and associated word problems.
• Use of parentheses with the order of operations.
• Find the volume of a cuboid by applying the appropriate formula.
  • Solve associated word problems.
• Recognize that rectangles with the same area can have different perimeters and vice versa.
• Students use two-dimensional coordinate grids to represent points, graph lines and simple figures.
• Know that 90 degress, 180 degrees, 270 degrees and 360 degrees represent a ¼ turn, ½ turn, ¾ turn and full turn.

 5^th Grade:

• Compute positive integer powers of nonnegative numbers.
• All four operations of decimals
• Fractions
  • Addition and subtraction of Mixed Numbers
  • Product of a Fraction and a Whole Number
  • Product of Fractions
  • Division of fractions
• Finding the area of a triangle
• Ratios
  • Finding ratios
  • Equivalent ratios
  • Comparing three quantities
• Finding unknown angles like supplementary angles
• Percent
  • Writing fractions as a percentage
  • Percentage of a quantity
• Average
• Rate
• Parallelograms and rhombuses – understanding angle and side relationships
• Volume of a solid
  • Finding the volume of a displacement
• Write and evaluate simple algebraic expressions
• Derive and apply the volumes and areas of simple objects.
• Know that the sum of angles in a triangle is 180 and the sum of angles in a quadrangle is 360.

 6^th grade:

• Compare and order all nonnegative and negative integers, fractions, decimals and mixed numbers.

• Ratio and Fraction
• Ration and Proportion
• Changing Ratios
• Percentage
  • Part of a whole as a percentage
  • One quantity as a percentage of another
  • Discount sales, interest earned and tips
• Speed and average speed
• Convert one unit of measurement to another. (inches to centimeters, feet to miles)
• Know how to convert from Celsius to Fahrenheit and vice versa.
• Know and use formulas for triangular prisms and cylinders.
• Identify angles as vertical, adjacent, complementary or supplementary.
• Be able to solve unknown angles using complementary or supplementary angles.

          From  Amy Flax, Westfield, NJ parent and math teacher

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1) P. 8 of the Massachussetts standards state under Guiding Principles for technology (my concern here is use of calculators which is mentioned in our NJ standards at grade 2 but I know is used even earlier - I didn't see calculators mentioned in MA up to and including grade 4 in the Number Sense and Operation strand): 

 Technology enhances the mathematics curriculum in many ways. Tools such as measuring instruments, manipulatives (such as base ten blocks and fraction pieces), scientific and graphing calculators, and computers with appropriate software, if properly used, contribute to a rich learning environment for developing and applying mathematical concepts. However, appropriate use of calculators is essential; calculators should not be used as a replacement for basic understanding and skills. Moreover, the fourth and sixth grade state assessments do not permit the use of a calculator. Elementary students should learn how to perform thoroughly the basic arithmetic operations independent of the use of a calculator.⁷ Although the use of a graphing calculator can help middle and secondary students to visualize properties of functions and their graphs, graphing calculators should be used to enhance their understanding and skills rather than replace them.

 2) For Grades 1-2:

    A)  MA has students represent money up to $5.  NJ is up to $1.

    B) MA has add and subtract 3-digit numbers.  NJ .  NJ is add and subtract 2-digit numbers.

    C) MA states "...ability to use the conventional algorithms for addition (two 3-digit numbers and three 2-digit numbers) and subtraction (two 3-digit numbers).  NJ says "efficient and accurate" but mentions nothing about "conventional".  MA also mentioned efficiency and accuracy.

 3) For Grades 3-4:

    A) MA has add and subtract up to 5-digit numbers and multiplay up to 3-digits by 2-digits.  NJ is adding and subtracting 3-digit numbers in grade 3 with no explicit mention of addition and subtraction in grade 4.  NJ is multiplication of 2-digit numbers.

    B) MA states "...ability to use the conventional algorithms for addition and subtraction  (up to five-digit numbers), and multiplication (up to three digits by two digits).  NJ says "efficient and accurate" but mentions nothing about "conventional".  MA also mentioned efficiency and accuracy.

  In addition, Massachussetts has a Harvard math professor involved as the mathematics advisor.  Does New Jersey engage a Princeton math professor?  Also, there was a public comment period in Massachussetts.  Does New Jersey also offer this period for the public to review the document?  I know you specifically requested to review but that is different than offering it globally.

Jackie Barlow, Bridgewater, NJ

-----------------------------------------------------------------------------------------------------------------------------------Read our Analysis of CMENJ_ Major Concerns.doc