Common Core math standards should include higher standards for students who hope to major in science, technology and math disciplines, says the U.S. Coalition for World-Class Math. In a Curriculum Matters comment, Barry Garelick wrote:

. . . we believe that less emphasis be placed on statistics, probability and modeling, in order to allow for the content that students pursuing STEM fields will need.

In fact, the coalition believes the proposed standards don’t meet requirements for humanities and social science majors at many state universities.

See also a discussion of fixing math and science education in the Wall Street Journal with New York City Chancellor Joel Klein, Amy Gutmann, president of the University of Pennsylvania, and Christopher Edley Jr., dean of the Berkeley law school and a member of Obama’s transition team.

That would certainly be lovely. Meanwhile, however, we have many thousands of 18-year olds across the country (not to mention many millions of adults) who are not competent in basic, 8th grade-level (pre-Algebra) math.

Perhaps we’ve been approaching this whole thing incorrectly. Instead of setting ridiculously rigorous standards that our school simply can’t meet (and are therefore compelled to lie about and game their way out of), perhaps we should be setting as our initial goal proficiency at 8th grade standards for all 18-year olds. If we could guarantee that within 10 years, say, all HS graduates could read and write at the 8th grade level, and do basic, 8th grade math proficiently, we’d be in a far better place than we are in now. And if we wanted to aim higher at that point, we could begin pushing things up.

But let’s be honest–that’s not a guarantee we are even close to being able to make. Not this year, and probably not in five years, sadly. But it’s a more reasonable goal to aim for, isn’t it? At least as a first step?

I disagree with the suggestion to place less emphasis on statistics and probability. Understanding statistics is a necessity for modern life, and certainly a necessity for students pursuing fields like history or international relations. Very few people actually need to know how to compute the area of a pentagon, but everyone needs to understand what a margin of error means.

I also believe that statistics are very important. My 6th grader just spent the first 2 months of the year learning stats. As an engineer, I can say that use statistics daily – more than any other math.

Don’t get side-tracked by statistics. The problem is not what skills an average student needs by the end of high school. It has to do with closing educational doors. The Common Core standards do not address this problem. If a student struggles with reaching Algebra II skills by the end of high school, he/she will not be prepared for most college STEM programs. The student will be at a peak rather than a base camp. A better definition of math standards should start back in K-8, with the key door being a proper course in algebra by 8th grade; 9th at the latest. Kids and parents need to know where these doors are and schools can’t be cavalier about the future potential or career interest students might have.

In terms of statistics, kids are NOT statistics. They are individuals. K-12 schools should be all about opening individual educational doors, not statistically closing them. Ironically, by trying to raise terminal math standards in high school, they allow school systems to ignore the source of all problems in math; fuzzy K-8 math curricula.

With a proper achievement of algebra by 8th or 9th grade, many other options (doors) will be available for students in high school. If a student decides to pursue a STEM degree in college, he/she is ready to follow the AP calculus track. If a student wants to pursue a non-technical career, he/she can focus on other courses, or even take some specialized course in statistics. If a student decides to pursue a vocational career, he/she won’t be stuck in a Groundhog Day-type of cycle trying to get past Algebra II.

I totally disagree with this statement. We live in a data driven society, students should be taught how to interpet graphs and data. How are we going to have a society of informed citizens if we do not teach Statistics (Data Analysis) and Probability.

Analyzing data and coming up with models aids in a students critical thinking and most important can see a conncetion to Algebra.

Besides, if everyone understood probability, state lotteries would die out for lack of participants…

Our comments did not suggest eliminating statistics, but placing less emphasis on it. Data and graph interpretation is important; stem and leaf, and box and whisker plots are not. Also, at this stage of learning, mastery of key mathematical concepts and problem solving techniques are essential, whereas a statistical estimation approach to problem solving is not. The quote about statistics in Joanne’s write-up above was part of a longer paragraph which said:

“Many mathematicians believe that statistics, probability and modeling are, for the emost part, non-essential for college readiness. These subjects are taught quite well in colleges, and students will gain the proficiency in these topics as needed.”

Why would we want to see more topics in, say, algebra 2 covered rather than the current emphasis on stat, probability and modeling as the Common Core draft recommends? Because enrollment prerequisites for BA programs in non-STEM fields of many, perhaps most, state universities also require mastery of numerous Algebra II topics that are not included in the current draft. This includes the California State University and University of California systems, the University of Texas and Texas A&M systems, University of Illinois and Illinois State University systems, Florida State and University of Florida, Ohio State University, and many others.

The omission of significant portions of essential Algebra II and Geometry content renders the Common Core Standards inadequate for students who will enter undergraduate programs in STEM or even non-STEM disciplines in much of the country.

If a child does not know how to add,subtract, multiply and divide, any higher math and understanding of it will not happen.

that includes algebra, stat, etc..

teaching a k-8 to estimate the answer and not know how to do it, is a disservice to the child.

There are steps that need to be followed, a logical progression from add to subt, to multiply, to divide, to one variable, to the next…. to stat, but unfortunately, a majority of states math standards no longer have the road map that was used in the past and is still being used in countries that outscore us on the PISA and TIMMS.

Instead, a child is introduced to concepts fleetingly when they sould not be, just for the sake of it with no mastery.

How can we expect our children/students to be mathematically compentent, succeed in math when they are first attempted to be taught to ride a bicycle before they can even walk.

The problem as Barry so rightly tried to explain is that the mile-wide, inch-deep approach to math prevents mastery – whether in high school, or lower grades.

By 3rd grade this means mastery of addition/subtraction.

By 5th grade this means mastery of multiplication/division.

etc…

Checkout page 20 of the Final Report – National Mathematics Advisory Panel – Benchmarks for the Critical Foundations

http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

This isn’t just Barry’s opinion. Its the best available scientific evidence for achievement. Focus on mastery of key topics at key points in a student’s academic career – not this destructive spiraling where kids do “statistics” in 6th grade. Master multiplication and division of fractions and decimals in 6th grade – and take a real statistics course later.

It is important to remain focused about what really is at stake here. Yes, statistics are important. However, succeeding in algebra by 8th grade is the most significant predictor of future math success. As the US Coalition noted in their addendum to their initial response about the Common Core draft, both STEM and non-STEM students need to exhibit a solid proficiency in math to graduate.

Changing the curriculum to less rigorous material only lies to the students making each believe he or she has a mastery of the subject when no mastery actually exists. And, the educational gap widens.

A solid education begins in the elementary school years and continues as the student climbs the ladder. Anything less results in a stagnant student and a stagnant environment. Do we want this?

There are three points to the World-Class math argument.

One, if you want STEM preparedness for college, then the curriculum has to be rigorous. For example, Algebra 2 as assessed by Achieve and/or the standards in the NMAP Final Report.

Two, since getting to rigor is tough, removing less important items from the curriculum is smart. While nice, box & whiskers, etc. are basically cute dead-ends in middle school. They don’t need to be taught.

Three, the proposed Common Core standards are too weak to prepare for STEM in college. They may be ok as a high school graduation requirement for a non-college prep diploma, if levels of diplomas are issued by a state. This is actually a different issue. Still, if only one diploma is offered, then World Class proponents would say that it should be rigorous, Common Core says “ehh, let’s make it look hard and say that it is hard; that’s enough.”

Statistics in many elementary and middle school classrooms translates into probability experiments like flipping coins to determine the likelihood of an outcome. While I’m not opposed to teaching real mathematical statistics, such as margin of error and data analysis, that’s not what’s being taught at these levels. Many K-8 teachers don’t even understand these mathematical concepts themselves, so it’s naive to think students will receive a robust statistics education.

I have carefully gone through the Common Core college and career readiness standards as well as the U.S. Coalition for World Class Math’s comments. I am in complete agreement with the Coalition’s position, especially with regard to the probability, statistics, and modeling standards. Probability and Statistics comprise 20% of the standards and 24% of the Core Skills are in those two areas.

How necessary are the topics of Probability and Statistics to college readiness? Look on page 12 of the report given below to see what one mathematician says to “How Much DASP Do Students Need?”

Stars by Which to Navigate:

Scanning National and International Standards in 2009

AN INTERIM REPORT ON COMMON CORE, NAEP,

TIMSS AND PISA • OCTOBER 2009 The Thomas B. Fordham Institute

http://www.edexcellence.net/index.cfm/news_stars-by-which-to-navigate-scanning-national-and-international-standards-in-2009

Over the years I have seen more and more statistics and probability creep into K-12 math textbooks and programs. Some of it is not addressed well mathematically or is addressed without students yet having prerequisite knowledge. I would rather students at earlier levels gain a solid foundation with their math skills.

It is important to understand statistics in today’s world. However, I agree with Todd Hausman I wonder how many K-8 math teacher really understand these mathematical concepts. I as a math professor at a university, and am teaching math education students. I have seen so many K-8 math teacher struggle with these concepts. I would not bet a dime on it. I also agree with Barry Gstrlick’s comments about we need to cover the basic topics first and in greater depth. Then we can dream about the more advance topic in statistic, probability and modeling. We need our students to be able to walk before they can run.

Barry and Todd are absolutely correct. The emphasis should be on learning basics in the lower grades. Let the college professors that have dedicated their lives to the study of statistics and probability instruct students who are ready to learn these skills.

Pat Murray

I was in a meeting two days ago with a teacher of 32 years, who had never heard the term outlier before.

Firstly, Todd Hausman’s reply about the quality of probability and statistics education is exactly correct. Rolling dice does not mean useful statistics education in any way or shape and Cardinal Fang and Therese should keep this in mind when emphasizing the importance of statistics education.

Further as Barry Garelick himself says above, he was simply stating the importance of other math topics over placing excessive emphasis on rolling dice and drawing pie charts in the classroom.

Please read Mr Garelick’s full comment a bit more carefully: http://roomfordebate.blogs.nytimes.com/2009/10/15/how-to-improve-national-math-scores/#barry

The emphasis is “content over process”. This emphasis is definitely NOT in the core curriculum proposed. Their emphasis remains “process over content”. One simply needs to try to solve their sample problems!

See for example:

http://www.corestandards.org/Files/MathExamples/05Equations.pdf

Work through a couple of these examples, please!

Our children do not know the multiplication tables. They do not understand that 2/3 is not “2 over 3” but two-thirds and so they so not understand how to work with fractions. They do not know the order of operations and will write 2+3*4=24 without hesitation. They do not differentiate between simplifying an expression and solving an equation (my blog on this and the core standards at: http://www.mathcasts.org/janita/?p=213). They do not define variables with units and thus will write expressions that combine pounds and dollars. Etc., etc….

Instead they solve “rich problems” that take 1/2 hour just to read (e.g problem 25 from above link from the proposed core standards), are given problems with ready-to-use functions (e.g. example 3 from same link) to just plug (and pray) without thinking or interpreting and problems that involve mathematical “tricks” (e.g. examples 2, 4 and 5 from same link).

Finally, they are given partial credit according to complex grading rubrics and thus pass courses without ever having solved an entire problem correctly.

Content over process!

Sorry that was supposed to read: 2+3*4=20. I am bad at bad math 🙂

An outlier is when a number in a set of data is much greater or much smaller than the rest of the data. For example the data set of 67,69,72,105; 105 would be the outlier because it is much greater than the rest of the data.

This is so insignigicant and yet my children started learnig about the mean, median, mode, range and outlier since third grade and they are still learning about it in seventh grade. This is how they are wasting our childrens valuble time, by learning the same thing over and over again. By now my children could of already learned many other concepts.

The level of statistics taught in elementary grades serves to take valuable time away from foundation skills needed for further progress in math. Time is a precious commodity, but the programs our students currently muddle through seem to think they have all the time in the world to catch-up. Unfortunately, by the time most kids get to the end of high school it is too late. Any hope of getting into an engineering, math, or science program is a dream.

The common core standards are a mirage. They further water down the education are students receive but call it progress.

Andrew, you are so, so right.

“…yet my children started learnig about the mean, median, mode, range and outlier since third grade and they are still learning about it in seventh grade.”

A friend of mine once complained that her three kids (in different grades) were covering the same material in math. Guess which curriculum I’m talking about. Yup, Everyday Math. It’s what I call repeated partial learning. The problem is not statistics. It goes much deeper than that. It’s about a dislike of content and mastery of skills. They want math to be a pump and not a filter, so they buy into spiral curricula like EM and then “trust the spiral”. Once kids get old enough (7th grade), it’s easier to blame the kids (and parents and society and poverty). All they do is point to the kids who are doing well. They should ask those kids why they do well. My son would tell them that his father was the one who used Singapore Math at home and ensured mastery. And they wonder where the academic gap comes from.

I talked to a 5th grade teacher the other day who said she graduated college with a degree in education and had no idea how to multiply/divide/add/subtract fractions.

Something is wrong when you can graduate college with a degree in teaching and not know basic math facts!!

Then I have to listen to school board members gleefully say how happy they are that 3rd graders are learning geometry and algebra! Really? Because when I taught algebra the best students knew their math facts. They memorized their math facts and knew how to mulitiply/divide fractions which is CRITICAL in algebra. This same school board member ignored the fact that their school used Everyday math which doesn’t allow for mastery of basic math facts.

I guess she’ll find out the hard way, when her kids get to high school and can’t work algebra problems because they have no idea how to multiply/divide fractions!

In response to Andrew, all states already have standards which are at least designed to reach an 8th grade level of proficiency. And look at where that has gotten us. Do you really want to guarantee that we remain below most other countries on the international tests?

The high number of students needing remedial math in college is a discrace, especially when statistics show that they are far less likely to graduate from college than those who are already prepared for college math. None of these remedial students failed their math placement test because of a lack on knowlege about “statistics”. They failed because they lacked basic skills. Let’s keep our priorities straight.

When my son’s 8th grade state tests came in, I found it interesting that he had missed almost half of the “probability” and “data” questions in the math section. Since he is accelerated (pre-algebra by 4th grade, algebra in the 5th), he missed out on the years of marble guessing, stem and leaf plots, and baby stats. He did, however, get a lot of algebra after demonstrating that he had mastered arithmetic.

The main reason I found it funny is that he’s presently making A’s in his AP Stats class as a freshman in high school, even though according to the state tests, he has a problem.

I don’t think he still knows what a stem and leaf plot is.

The whole idea that “everyone” should have algebra I in 8th grade, because it leads to various successes down the line, is based on a flawed assumption. The original findings that kids who took algebra I in 8th grade did better on SAT, GPA or whatever else, was an entirely predictable CORRELATION. At that time, ONLY the kids on the honors/AP math track took agebra (typically offered only at honors level) in 8th grade. It was therefore to be expected that they would do better on various other measures, as well; 8th-grade algebra was merely a proxy variable for identifying the top of the academic pile. The rush to assume a causal relationship was also seen with self-esteem, 6th-grade Latin, debate team, number of books at home etc., as well. Algebra, more often “algebra”, in 8th grade is not a magic bullet.

That being said, I am sure that far more kids can be PREPARED AND READY for it; that means mastery of all the foundational knowledge and skills. A significant number of kids will be ready by 6th or 7th grade, more in 8th and some not until later. Half of all kids are below average and some of them would be much better served by mastery of math through fractions, decimals and percentages by the end of 8th grade. That would be better than fake algebra built on sand.

“That would be better than fake algebra built on sand.”

This is a strawman. Nobody is talking about fake algebra, although that’s what many students get nowadays. The NMAP defined a proper course of “School Algebra” that should be reached by 8th or 9th grade (at the latest) for most all students. A goal of fractions, decimals, and percentages by the end of eighth grade is just not enough. This is a sixth grade goal.

Most schools provide slower routes usually based on an end of 6th grade math track placement test, but the slower tracks are often tracks to nowhere because the kids are still struggling with big gaps in their basic skills and knowledge. A slower track doesn’t fix a bad curriculum. The kids who get on the top math track usually get help at home or with tutors.

The problem is not that schools don’t offer algebra I in 8th grade. The problem is that they are often watered down and the schools don’t think that most kids are smart enough to get there. The goal of the NMAP was to define what a proper course in algegra is and when most students are capable of taking it. This tackles the problem of watered down algebra courses, but it doesn’t apply much pressure on schools to fix their lousy K-6 math curricula. Setting the goal of mastery of fractions, decimals, and percentages by the end of 8th grade doesn’t ensure mastery or force any changes in the lower grades, and it waters down the expectations. The assumption seems to be that if you give schools more time, then proper mastery will happen. Not a chance.