Information Age Education
   Issue Number 185
May, 2016   

This free Information Age Education Newsletter is edited by Dave Moursund and Bob Sylwester, and produced by Ken Loge. The newsletter is one component of the Information Age Education (IAE) publications.

All back issues of the newsletter and subscription information are available online. In addition, six free books based on the newsletters are available: Validity and Credibility of Information; Education for Students’ Futures; Understanding and Mastering Complexity; Consciousness and Morality: Recent Research Developments; Creating an Appropriate 21st Century Education; and Common Core State Standards for Education in America.

This newsletter is not part of the Joy of Learning series that began several months ago and will continue for several more months. The editors felt that the content presented below is sufficiently important so that we should not wait until the end of the Joy of Learning series to share it with you.


Math Education for Preservice Elementary School Teachers

David Moursund
Emeritus Professor of Education
University of Oregon

This IAE Newsletter is about the math preparation of students enrolling in a college program designed to prepare elementary school teachers. In the United States and in many other countries, a typical elementary school teacher is responsible for teaching math, science, language arts, social studies, and perhaps other subjects. Thus, a great many elementary school students learn math from a teacher who is not a math specialist.

A typical student entering the elementary education teacher’s program has had three or four years of high school mathematics and has met the requirements to be admitted to a college or university. The math and math methods required in this program of study vary considerably. A “strong” program of study may require a yearlong Mathematics Department course, such as Mathematics for Elementary Teachers, which has a prerequisite of College Algebra or its equivalent. A strong program may also require a yearlong Curriculum and Instruction course, such as Math Methods for Elementary Teachers.

Weaker programs may require less Mathematics Department coursework that has little or no math prerequisite, and less than a year of College of Education coursework in Math Methods.

You might ask the question: Why is so much math content and pedagogy required? After all, even before starting college, a typical prospective K-5 teacher has had six or seven years of math in grades 6-12, and has observed and participated in how math is taught for 11 or 12 years.

The simple answer is that the math content and pedagogy knowledge and skills required to be competent in teaching today’s elementary school math curriculum are large and challenging. Researchers and practitioners have accumulated a huge—and steadily growing—body of knowledge that can contribute to being a good math teacher.

And, don’t forget the potential impact of calculators and computers as an aid to teaching, learning, and using math. I have spent most of my career working in this area (Moursund, 2016a; 2016b; 2015). Currently, most preservice and inservice teachers of elementary school math are woefully underprepared in the computer field.

In addition, there are the challenges of working with special education students, talented and gifted students, and students who are just in the process of learning English.

Some countries, such as China, use math specialists to teach elementary school math (Pine, 7/13/2012). Such specialists have far more preparation in math content and pedagogy than the “strong” program mentioned above, and they teach only math. This means that they gain on-the-job math teaching experience considerably more rapidly than do generalists who teach four, five, or more subjects per day.

A Personal Story

Early in my professional career, I became interested in teaching inservice math teachers about uses of computers in secondary schools. I learned on the job, and eventually expanded my computers-in-education interests to all K-12 discipline areas, as well as to teacher education for preservice teachers. I taught the Mathematics for Elementary Teachers yearlong sequence, and I sat in on a one-term Math Methods for Elementary Teachers course. In both of these teaching/learning experiences the poor level of math preparation of the preservice teachers surprised me.

The teacher of the Math Methods for Elementary Teachers course was a superb teacher of teachers. One day she had the students divided into groups working on a math problem she had posed. One of the groups that presented their work clearly did not know and understand the sixth grade math that they needed to solve the problem.

And, I remember the day that one of my grade school daughters asked me why her answer to a math problem had been marked as wrong. The sixth grade teacher was teaching about bases other than base ten—and the teacher was clearly wrong.

I encountered situations like these over and over again while teaching Mathematics for Elementary Teachers. Clearly the students had taken precollege coursework on a number of the topics I was covering—but they no longer had the knowledge and skills that they had demonstrated in these classrooms a few years earlier in their schooling.

A 2015 report indicates that 90 percent of adults in the U.S. have a high school diploma or a GED (U.S. Census, n.d.). Yet, in the U.S., the “average” adult performs at about the eighth grade level in both reading and math (PRNewswire, 3/10/2016; Wikipedia, n.d.). To a large extent, this is an example of “use it or lose it.”

Elementary School Math Education at Southern Illinois University Carbondale

The remainder of this newsletter focuses on a report, Computational Skills and Understanding (Becker, Fall, 2014). Jerry P. Becker is a highly respected math educator. Through his work and the work of others at Southern Illinois University Carbondale, the Math Methods and Math Content courses for preservice elementary teachers are jointly taught and are cross-listed by the Department of Curriculum and Instruction in the College of Education and the Mathematics Department. The four semester-length courses are CI/Math 120, CI/Math 220, CI/Math 321, and CI/Math 322. Both interdepartmental team teaching and faculty from one department teaching in the other department are part of this arrangement.

In Becker’s research, a 50-item arithmetic Pretest was given the first day of the CI/Math 120 class in Fall, 2014 (Becker, Fall, 2014). This was strictly a paper-and-pencil test—students were not allowed to use calculators. It was not a multiple-choice test—students had to determine and write their answers. Students were given as much time as they wanted to complete the test.

The complete test along with data and analysis is available in Becker’s paper. Here are a few Pretest test items on which students did poorly.

Question
Percent of
incorrect answers

1/9 - 5/13 =
78% incorrect
4.8 - 6.2 =
78% incorrect
2 1/5 divided by 4 1/3 =
80% incorrect
Express .225 as a fraction
98% incorrect
6 x 2. =
87% incorrect
1/5 x (-89)
76% incorrect
5/6 + 1/7 =
61% incorrect
9.5 / .5 =
74% incorrect

Three weeks of three 50-minute classes per week were used in re-teaching elementary and middle school arithmetic. After that, a Posttest was administered. It was the same as the Pretest, but the numbers were changed.

Quoting from Becker’s paper:

There were 15 Freshmen, 14 Sophomores, 12 Juniors, 1 senior and 2 exchange students (China) in the two sections of CI/Math 120. [Note: The two Chinese students got near perfect scores on the pretest and perfect scores on the posttest.]

There were 50 problems (50 points) on the test, nearly all concerned with problems of simple addition, subtraction, multiplication and division of whole numbers, integers [positive and negative numbers], fractions and decimals.

[T]he median score for the two sections on the Pretest is 28, so half of the students scored less than 28 on the Pretest.

There were no perfect scores and the highest scores were in the low 40s.

The results on the posttest were improved. Here the median was just under 42, so half of the students scored less than 42; 75% scored below 45. The lowest score was 15 (out of 50). There were several students with scores of 50.

Some of My Thoughts

I don’t find these results surprising. Colleges and universities have long made use of math placement tests that lead to a significant number of students needing to take remedial math courses (Moursund, 2/2/2015). What Becker and his colleagues decided to do was to use three weeks of the CI/Math 120 course to remediate this situation, rather than to require the students to spend a semester taking a remedial course.

I noted that three weeks of instruction and practice raised the median score from 29 to about 42. The initial scores provide a good example of “use it or lose it.” Most secondary school and older students do not encounter such computational tasks very often.

Indeed, many of the arithmetic problems on the test are not ones that I encounter in my everyday life, and I expect the same statement holds for you unless you teach arithmetic. This makes me wonder about the wisdom of placing so much K-8 curriculum emphasis on computational arithmetic. The new Common Core State Standards place an increased emphasis on learning for understanding, rather than on rote memory for fast, accurate, by-hand arithmetic calculation.

My personal approach to the situation encountered by Becker and his colleagues throughout the math education community would consist of the following:
  1. Provide students with good self-assessment tests. (A good test provides links to self-instruction materials.) Tell the students that, if they want to become an elementary teacher, they are responsible for learning or relearning the material on the test.

  2. Do not use valuable class time teaching the elementary and middle school materials that are prerequisites for the required math content and math methods courses. Rather, expect and require students to relearn the required arithmetic skills on their own.
Here is one point that I find disturbing. Even after three weeks of instruction, half of the students scored below 42 (that is, below 84%) on the test. That raises an interesting question. Do we want our children to be taught arithmetic by teachers who are not themselves very good at doing arithmetic?

As noted earlier, I have long been a proponent of the use of calculators (and computers) as an aid to solving the types of problems one is studying in school. I certainly would have liked to see how well the students in Becker’s research would have performed if they had been allowed to use calculators on the test.

Final Remarks

Becker’s paper provides a number of suggested ideas about why students entering the teacher education program are not better prepared. The three subsections given below are a summary (a combination of quotations and paraphrases) of several observations by Jerry Becker and his colleagues.

Teacher knowledge/understanding accounts for some of it.

In some cases, we wonder if teacher knowledge/understanding is a factor. We mean this in the sense of Dr. Liping Ma’s book, Profound Understanding of Fundamental Mathematics, for the full spectrum of elementary and middle school mathematics, not only computation and arithmetic facts. [See http://www.nytimes.com/2013/12/18/opinion/q-a-with-liping-ma.html?_r=0.] This applies to high school as well, but we THINK teacher knowledge/understanding is less of a problem at the high school level.

More students enter college.

This would mean that more students weaker in computational skills (mathematics) are in college than used to be the case. Some (many?) of them are finding their way into teacher education programs. This might be especially true for many students coming to higher education from large urban school districts.

It’s not the students’ fault.

Whatever weaknesses these students have when they reach us at the college/university level, it is not their fault. They have come out of school systems with a diploma. Also, here at Southern Illinois University Carbondale they have been admitted to a major comprehensive research university and one has to wonder how this can be. [Bold added for emphasis.]

I disagree with Becker on this fault-assigning point. My personal opinion is that our K-12 schools should regularly emphasize to their students that student learning is a combined responsibility of the educational system and the student. It is certainly partly the fault of precollege students that they are not adequately gaining the knowledge and skills that the school is teaching.

I find it quite interesting that the SIUC teacher education program has faced the problem directly and is working to meet the needs of the students. Many colleges and universities are not so forthright.

As a closing final remark, I am sure that elementary teacher education programs face similar problems in preparing students to teach English Language Arts and the sciences. The writing skills of most high school graduates are sufficiently weak that many colleges require students to take a year of English Composition no matter what their intended major.

References and Resources

Becker, J.P. (Fall, 2014). Computational skills and understanding. Retrieved 4/18/2016 from http://mathforum.org/kb/servlet/JiveServlet/download/323-2767606-9903743-1257428/R%20PDF%20Brief%20Report%20Computation%20Understanding[1].pdf.

CDC (n.d.). Understanding literacy and numeracy. Center for Disease Control and Prevention. Retrieved 4/24/2016 from http://www.cdc.gov/healthliteracy/learn/understandingliteracy.html.

Moursund, D. (2016a). Math methods for preservice elementary teachers. IAE-pedia. Retrieved 4/24/2016 from http://iae-pedia.org/Math_Methods_for_Preservice_Elementary_Teachers.

Moursund, D. (2016b). Math maturity. IAE-pedia. Retrieved 4/24/2016 from http://iae-pedia.org/Math_Maturity.

Moursund, D. (2016c). Communicating in the language of mathematics. IAE-pedia. Retrieved 4/24/2016 from http://iae-pedia.org/Communicating_in_the_Language_of_Mathematics.

Moursund, D. (3/23/2016). Math word problems. IAE Blog. Retrieved 4/24/2016 from http://i-a-e.org/iae-blog/entry/math-word-problems.html.

Moursund, D. (2015). Computational thinking. IAE-pedia. Retrieved 4/24/2016 from http://iae-pedia.org/Computational_Thinking.

Moursund, D. (2/2/2015). Are high school seriously misleading our students? IAE Blog. Retrieved 4/24/2016 from http://i-a-e.org/iae-blog/entry/are-high-schools-seriously-misleading-our-students-update.html.

Moursund, D. (6/26/2014). Improving math education. IAE Blog. Retrieved 4/24/2016 from http://i-a-e.org/iae-blog/entry/improving-math-education.html.

Pine, N. (7/13/2012). Specialist teachers in elementary classrooms? Huffpost Education. Retrieved 4/24/2016 from http://www.huffingtonpost.com/nancy-pine/specialist-teachers-best-_b_1669799.html.

PRNewswire (3/10/2016). U.S. adults below international average in numeracy and digital problem-solving skills; Average in literacy. Retrieved 4/24/2016 from http://www.prnewswire.com/news-releases/us-adults-below-international-average-in-numeracy-and-digital-problem-solving-skills-average-in-literacy-571648161.html.

U.S. Census (n.d.). Educational attainment in the United States: 2015. Retrieved 4/24/2016 from https://www.census.gov/hhes/socdemo/education/.

Wikipedia (n.d.). Adult literacy in the United States. Retrieved 4/24/2016 from https://en.wikipedia.org/wiki/Literacy_in_the_United_States.

Author

David Moursund is an Emeritus Professor of Education at the University of Oregon, and coeditor of the IAE Newsletter. His professional career includes founding the International Society for Technology in Education (ISTE) in 1979, serving as ISTE’s executive officer for 19 years, and establishing ISTE’s flagship publication, Learning and Leading with Technology. He was the major professor or co-major professor for 82 doctoral students. He has presented hundreds of professional talks and workshops. He has authored or coauthored more than 60 academic books and hundreds of articles. Many of these books are available free online. See http://iaepedia.org/David_Moursund_Books. In 2007, Moursund founded Information Age Education (IAE). IAE provides free online educational materials via its IAE-pedia, IAE Newsletter, IAE Blog, and books. See http://iaepedia.org/Main_Page#IAE_in_a_Nutshell.

Email: moursund@uoregon.edu.

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