# Common Core and Progressive Domination of Math Instruction Equals Mathematic Illiteracy

A century of progressive domination of the American educational system has resulted in a growing number of Americans remaining mathematically illiterate. The Common Core standards are a repeat of previously failed federal policies which fail to develop academic skill making the study of mathematics needlessly boring and challenging for too many talented students. These federally supported educational policies have left our society short of talented mathematicians needed to make the American economy competitive with other nations.

Once again, the Common Core Standards are another federal policy which discourages students from memorizing multiplication facts and other basic math theories and formulas. These policies are in place to justify the emphasis on student-centered, discovery, and inquiry methods of instruction which fail because they are laborious, error-ridden, discouraging methods for introducing new concepts to young learners according to research.

The discovery and inquiry methods of instruction are useful only when a student has the basic skills needed to become “creative’ with the use of that skill. For example: when a child is asked to discover the solution to 8 X 7 instead of memorizing the fact that 8 X 7 is 56, the student uses a variety of techniques to discover the answer. Grouping of eight or seven objects, counting on fingers, etc. are the processes often used.

When this laborious action is promoted and the memorization of facts is discouraged, solving a simple math problem becomes time consuming and error ridden making the learning of math frustrating and a hated task for too many students who could have become excellent mathematicians.

As a teacher, I quickly saw this flaw in the discovery and inquiry methods of instruction and refused to depend upon them in my classroom. Unfortunately, because other teachers were not requiring students to take time to memorize basic math facts, I had to spend considerable time proving to students that memorizing these facts would open the world of math to them. My approach is commonly called the direct instructional method.

I began by emphasizing the importance of learning how to memorize things; it is a skill that becomes easier with practice. Using their favorite rock stars, I pointed out that Michael Jackson, David Garrett (a crossover violinist), and Stevie Ray Vaughn play their music from memory. For a musician, memorizing the music enables fluidity. Memorizing math facts makes solving a math problem easier, faster, and more accurate.

If rock stars could memorize hundreds of songs, students could memorize 100 simple multiplication facts.

On a quiz comprised of ten basic multiplication problems and two very simple long division problems, the children who had learned long division using the discovery method during a previous school year used a dozen different methods for solving the problem. Few students obtained the correct answer using those methods. Their papers were covered with drawings and counting errors. Scores were low.

My students spent one week practicing multiplication facts in class because many parents were no longer willing to spend “family” time practicing these facts. Once the students mastered the basic multiplication facts from 0 through 10, I gave them the same quiz that I had given them earlier. Scores were improved significantly, and they finished the test in half the previous time.

Many students expressed surprise that long division problems were so much easier than they had originally thought. Some even noticed that division is the inverse of multiplication. This revelation could not have happened if they had not memorized their multiplication facts. I used this “teaching moment” to show my ten-year old students that they could now do pre-algebra. I put the following problems on the board:

3 X 7= 21

21=3 X 7

A X 7 = 21

21=3 X A

My students were amazed. I explained that, if they memorize a few basic facts, they will be able to see the relationships in numbers and the number patterns that make math a most amazing puzzle. Just as musicians must master chord progressions and a variety of techniques before they can create beautiful music, students must memorize some basic math concepts to unlock the mysteries of mathematics.

Having this basic knowledge would help students score well on an assessment test. The examples above proved to my students that they would be able to answer some basic algebra questions just because they mastered some basic math facts. Algebra is not required until the end of seventh grade in our district, but those who could answer some algebra questions on the test would rank among our highest performing sixth-grade students.

Students became self-motivated. Knowing that improving six points on the state exam would mean one full year of academic growth, many students set a goal much higher than that for themselves. Most met those goals.

State test results proved that my special needs students made the most progress once they memorized some basic math facts. These children are doers. They are easily frustrated. They resent mind games. They see school as a place where they are set-up for failure. Once students saw that memorizing facts was the key to accuracy and success, they made impressive progress.

Professor Kilpatrick and other progressive educational experts who have been shaping federal policies and promoting the federalization of our educational system are the source of the problem because they disrespect the American student. Kilpatrick is quoted as saying, “We have in the past taught algebra and geometry to too many, not too few.” If nothing else, a student of algebra learns that what is on one side of an equation must equal whatever is on the other.

Understanding this concept is essential for effective critical thinking.

Kilpatrick’s attitude is pervasive among American education experts and, therefore, prevails in federal educational policies.

It is time for civil disobedience. It is time for those who respect the intrinsic value of education and the right of every child to reach his academic potential to take back our schools at the local level.

http://revistas.pucsp.br/index.php/emp/article/viewFile/4686/3255

http://education-consumers.org/pdf/DI_Research.pdf

http://dataworks-ed.com/research-link-page/research/

Samuel Tennenbaum, William Heard Kilpatrick, Harper & Brothers Publishers, New York 1951. P. 105

**Karen Schroeder** is President of Advocates for Academic Freedom, a member of the Wisconsin Educational Communications Board, Member of WINNER board of directors, has a Master’s Degree in Special Education, and is an educational consultant. Contact Karen at: kpfschroeder@centurylink.net or by calling 715-234-5072.

THE EASY WAY TO REFORM EDUCATION

By Robert V. Rose, M.D. (retired) [email: rovarose@aol.com]

Historically, many authorities on the subject of literacy instruction have stressed the importance of adequate practice in printing alphabet letters. Marcus Quintinianus (a first-century Roman rhetorician) has been quoted as writing, that with regard to becoming literate, “Too slow a hand impedes the mind.”

In 1912, Maria Montessori wrote, in effect, that teaching young children to print letters is easy, that it is easy to teach children to read after they have practiced printing alphabet letters, but that it is difficult to teach children to read if they have not practiced writing them.1 Marilyn Jager Adams noted that prior to the onset of the twentieth century the “spelling drill” was the principal means of inducing literacy for several millennia.1

More recently, several published authors have called attention to the dearth of research on the possible link between printing practice and the acquisition of literacy in young children, but objective studies of the relationship are still lacking.2,3,4

This author has made the assumption that emphasis on practicing printing alphabet letters increases the fluency with which children can print them. It was therefore decided to examine the relationship between fluency at printing the alphabet in preliterate children, and their subsequent success in learning to read well.

This method suffers the disadvantage of requiring children to be able to recite the

alphabet in order to print the different letters both legibly and at a rate sufficient to demonstrate that they have practiced enough to have become “printing fluent.” However, it was considered superior to other methods of assessing fluency in printing alphabet letters in young children. Such children have limited attention spans. It was therefore decided to measure the number of alphabet letters children write during a timed twenty-second interval, and multiply that number by three in order to obtain a “letters-per-minute,” or “LPM,” value for each child.

During the early months of 2002, five first-grade teachers were enlisted from teacher-related Internet listservs, to do a cooperative study of the relationship between fluency in writing the alphabet, and concomitant reading skill.

The printing rate of each child was listed by teachers submitting classroom data, and each was matched by the subjective teacher assessment of the child’s relative reading skill. The assessments were A, B, C, D and E, to designate “excellent”, “above average”, “average”, “below average” and “possible reading problem”, respectively.

A total of 94 children in five first-grade classrooms were studied. When the letter grades were converted to numbers (4, 3, 2, 1, 0), “average relative reading ability” could be determined for subgroups of students, defined as printing at different rates.

Among the sixteen children who printed faster than 40 LPM, the average reading score was 3.6. Among the 33 children who printed from 30 to 39 LPM, the average was 2.9. For the 26 children writing at 20-29 LPM, it was 2.3. For the 21 children who wrote more slowly than 20 LPM, it was 1.6.

During this current school year, a number of kindergarten teachers have submitted series of similar studies on their classrooms to the k1writing listserv, accessible at

http://www.yahoogroups.com. By the end of February 2004, a total of five teachers had submitted serial data on a total of 106 kindergarten students, including data for the month of February.

The relative reading skills of the kindergartners were ranked according to a three-level system: “reading better than grade level”, “doing well at grade level” and “lagging behind expectations”. In the opinions of their teachers, six children were already reading at secondgrade level or above.

Statistical analysis of the correlation again yielded similar results. Among the eighteen children who printed the alphabet faster than 40 LPM, 72% were “above grade level,” and only one was “lagging.” Among the eighteen children who wrote more slowly than 20 LPM, none was above grade level in reading skill, and half of them were “lagging” in this regard.

A tabulation of these findings is revealing. It is informative to look down the column of LPM figures for these 106 children, and observe the correlations. These data are presented in Table One.

The correlation between reading skill and fluency at printing alphabet letters in

kindergarten and first-grade is readily apparent. This correlation was known to each of the experienced [kindergarten] teachers participating in this study even before the study was done. The experiment, then, was designed to answer the question as to whether this correlation is one of causation, or merely coincident with some other unidentified factor.

The kindergarten teachers involved have each been able to achieve a level of printing fluency that is considerably above what is generally achieved by American kindergarten students. The printing rates of their kindergarten children are comparable to the rates of the first-grade students in the original study, whose teachers had NOT been previously monitoring printing rate. If the cause of the correlation were in the opposite direction, and it is having learned to read which drives printing fluency, then one would expect the correlation to weaken in classrooms where printing fluency has been intentionally contrived. However, we here see the correlation has persisted intact.

This year, each of the kindergarten teachers has been making a dedicated effort to induce objectively measurable printing fluency in the students as the school year progresses. Each of the five kindergarten teachers has emphatically proclaimed that this practice is found to be immensely helpful in turning young children into readers.

A number of the classrooms have high percentages of poverty and minority children, and none of the children could read at the beginning of the kindergarten school year. It was found that printing fluency, which we arbitrarily defined as 40 LPM or faster, is achieved at different times by different children, and that such fluency is an excellent indicator of when children will learn to read, as well as indicating which children have become successful at reading at any particular point in time.

It was also observed that printing fluency gradually improves in almost all cases with continued practice writing the alphabet letters. Failure to cooperate during the time allocated by teachers for dedicated printing practice seems to be the main limiting factor in the development of printing skill.

None-the-less, our data suggest that fluency in writing the letters of the alphabet is a reasonable goal for all normal children by the end of first-grade.

But it appears that printing fluency does not at all correlate with reading ability much beyond the first-grade level. One teacher submitted data on 54 fourth-graders, demonstrating no difference at all in the median alphabet-printing rates between children who had been formally identified as reading below grade level, and the other students.5

It is also apparent that printing skill is by no means a necessary prerequisite for literacy.

Many children learn to read before they are fluent at printing alphabet letters. On the other hand, virtually all children who lag in reading skill in K-1 are dysfluent printers. That this lack of skill is remediable through continued dedicated practice, extended over time, appears to be of fundamental importance.

If the attainment of fluent ability to print alphabet letters in the earliest grades generally assures early success in reading, this fact challenges some current theoretical conceptions regarding the nature of reading disabilities.

Our evidence suggests both that printing fluency confers the ability to name random letters more rapidly than 40 per minute6, and that the ability to phonetically write words fluently, possible only after the attainment of fluency in printing letters, confers phonemic awareness.

Adams wrote, “It has been shown that the act of writing newly learned words results in a significant strengthening of their perceptual integrity in recognition. This is surely a factor underlying the documented advantages of programs that emphasize writing and spelling activities.”7

Montessori also considered practice writing alphabet letters to be crucial, and wrote, “We shall soon see that the child, on hearing the word, or on thinking of a word he already knows, will see, in his mind’s eye, all the letters, necessary to compose the word, arrange themselves. He will reproduce this vision with a facility most surprising to us.”7

And Ken Goodman in his book, What’s Whole About Whole Language, wrote “Children learn the alphabetic principle through writing”. And without understanding the alphabetic principle, literacy isn’t possible.

While such rhetorical explanations of the value of writing practice have been seen as nebulous in the past, converging advances in the fields of pattern recognition by artificial intelligence and of the cerebral physiology involved in visual pattern recognition and categorization may render them more plausible.

In 2012, Marilyn Jager Adams, the world’s leading authority on early literacy instruction, published ABC Foundations For Young Children, in which she presented newly published proof that most American children finishing first grade still can’t write and name all of the alphabet letters.8

This is a preventable disgrace, and Dr Adams emailed me these comments: “It’s hard to learn to read if you can’t tell one letter from another”, and “It’s strange that now, over 3,000 years after the invention of the alphabet, we still don’t know the best way to teach literacy”.

The best predictor of reading success in rising first-graders is the ability to rapidly name randomly presented alphabet letters, and Rand Nelson, on his blog, has shown that the best way to learn to rapidly name alphabet letters is to learn to handwrite them fluently first.9

And importantly, psychologist Rowe Young Kaple has now published her finding that most American children diagnosed as “learning disabled” actually suffer from a hereditary condition she calls Reverse Position Sensation (RPS) in which children previously considered “clumsy” feel a counter-clockwise motion of the hand as moving in the opposite direction. This often leads to difficulty learning to write (often called “dysgraphia” by teachers) unless the temporarily adopt a “remedial grip” of the pencil, by holding it between second and third fingers, forcing the palm to turn downward. (Many senior citizens are appalled that so many younger folks hold their writing implements in bizarre, abnormal positions).10

It is emphasized that these studies are limited and preliminary, but their results

underscore the pressing need to either confirm or disaffirm their apparent implications.

The author wishes to acknowledge the participation of the classroom teachers who did and submitted these comparison studies on their students. They are Libby Rhoden, Pasadena, Texas; Sue Fisher, Kailua Kona, Hawaii; Ann Vasconcellos, Homewood, Illinois; Helen Wilder, Middlesboro, Kentucky; Nancy Creech, Eastpointe, Michigan; Ruby Clayton, Indianapolis, Indiana; Alice A. Pickel, Phoenix, Arizona; Lori Jackson, Mission, South Dakota; Lalia Kerr, Nova Scotia; Jennifer Runkle, Ohio.

TABLE ONE

Kindergarten Students Printing Level in Letters Per Minute (LPM)

LPM rate:

> 40 LPM 30-39 LPM 20-29 LPM < 20 LPM

78** 39** 33** 27** 24* 18*

72** 39** 33** 27** 24* 18*

66** 39** 33** 27** 24* 18*

60** 39** 33* 27** 24o 18*

60* 39** 33* 27** 24o 18*

57** 39** 33* 27** 24* 18*

54** 39* 33* 27* 21* 18 o

54** 39 o 33 o 27* 21* 15*

51** 36** 30** 27* 21* 15*

51** 36** 30** 27* 21* 15 o

48** 36** 30** 27* 21* 15 o

48** 36** 30** 27o 21* 15 o

48** 36** 30** 27o 21* 12*

48* 36* 30* 24** 21* 12 o

48* 36* 30* 24* 21* 12 o

42** 36* 30* 24* 21 o 6 o

42* 36 o 30* 24* 21 o 3 o

42 o 30* 3 o

30*

In the opinion of respective classroom teachers:

KEY: o lagging in reading skill

* on level

** above level in reading

————————————————————————————————————–

References:

1. Montessori, Maria. The Montessori Method, Dover Publications, 2002, pp.266-7.

2. Adams, Marilyn Jager. Beginning to Read: Thinking and Learning About Print, MIT Press, 1990, p.388.

3. Sofia Vernon and Emilia Ferreiro. “Writing Development: A Neglected Variable in the

Consideration of Phonological Awareness.” Harvard Educational Review 69:4 (1999):

pp.395-415.

4. Groff, Patrick. “Teaching Phonics: Letter-to-phoneme, Phoneme-to-letter, or Both?” Reading and Writing Quarterly 17 (fall, 2001): pp.291-306.

5. Data provided by Marianne Morin, Watkins Glen, New York.

6. Data on kindergarten classroom correlation between letter-naming and printing fluency provided by Sue Fisher, Hawaii.

7. Adams, op. cit., pp 230-231

8. ABC Foundations For Young Children, introduction.

9. URL for the Nelson blog is: http://peterson-handwriting.com/Blog/

10. See URL: http://adderworld.ning.com/forum/topics/abstract-university-of-az

There are many things factually wrong with this article, which makes it difficult to take the author seriously.

This piece is based on a false premise: that fact fluency is not contained within the Common Core. It is, but I’d guess the author didn’t read them.

If she wants to argue that fluency should be moved to earlier grades, she could argue that.

Furthermore, nothing in the Common Core Math precludes the teaching of fact families like the one in her example.

There are many unwarranted premises in her commentary.

In Canada we have had a report released from the CD Howe Institute which validates this argument.

This is what started all the fuss http://news.nationalpost.com/news/canada/decline-of-canadian-students-math-skills-the-fault-of-discovery-learning-c-d-howe-institute

Massive response to this article. Parents, educators, and other concerned citizens are paying attention. Policy makers and educrats need to pay attention to what the public WANTS. We are paying for the system to exist. Time to start listening to us.

I didn’t particular understand this article.

Is Schroeder ignorant of the memorization required in CC?

Everything she mentions for memorization or fluency is already required by CC:

http://tncore.org/sites/www/Uploads/2.25.13Additions/fluency%20documents%20final.pdf

Required Fluency

K Add/subtract within 5

1 Add/subtract within 10

2 Add/subtract within 201

Add/subtract within 100 (pencil and paper)

3 Multiply/divide within 1002

Add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi‐digit multiplication

6 Multi‐digit division

6 Multi‐digit decimal operations

7 Solve px + q = r, p(x + q) = r

8 Solve simple 2×2 systems by inspection https://www.engageny.org/sites/default/files/resource/attachments/ccssfluencies.pdf

Schroeder and many others would benefit from watching the first hour (starting about 10 minutes in) of this video: https://youtu.be/BJoUEJazzJI

From what the above comment said about CC, expectations are way too low. At five, I taught my daughter how to add with carry, and she made up problems to play with. She was adding numbers like

50456298120345

21348759012594

and getting the correct answers. It makes the CC standards of addition cited above simply laughable. There’s no trick to going from adding 2-digit numbers to 20-digit numbers except the mental blocks in the mind of a teacher or curriculum designer. I didn’t teach subtraction to my kid but she got that in school.

I don’t know what CC constitutes, but the concept of number sense which kids are supposed to learn is mostly nonsense. It is not involved in the techniques for making fairly good estimates of the results of arithmetic operations.

CC should pay attention to 1) real professional mathematicians and 2) psychologists who study the basic cognitive skills of young children, keeping in mind that some catch on quicker and some slower. Going slow enough for the slow kids is likely to bore the hell out of the smarter kids. And that’s been an obvious problem of teaching for ages.

Interesting take.

Cuts against the grain.

The more common complaint is that the math standards are too difficult at the younger ages and too easy at the older grades (I disagree with both – since older students who are gifted should opt for calculus…).