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Research Developments;Creating
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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:
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.
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.
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.
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