Download ppt - What Important Mathematics do Elementary School Teachers “Need to Know”? (and)

What Important Mathematics doElementary School Teachers

“Need to Know”?

(and)

How Should Elementary School Teachers

“Come to Know” Mathematics?

Jim LewisUniversity of Nebraska-Lincoln

Math Matters

A Mathematics – Mathematics Education Partnership at the

University of Nebraska-Lincoln

Ruth Heaton and Jim Lewis

What’s the big deal?

Can’t any good elementary school teacher teach children

elementary school mathematics?

What is so difficult about the preparation of mathematics teachers?

• Our universities do not adequately prepare mathematics teachers for their mathematical needs in the school classroom. Most teachers cannot bridge the gap between what we teach them in the undergraduate curriculum and what they teach in schools.

• We have not done nearly enough to help teachers understand the essential characteristics of mathematics: its precision, the ubiquity of logical reasoning, and its coherence as a discipline.

• The goal is not to help future teachers learn mathematics but to make them better teachers.

H. Wu

What is so difficult ….?

• For most future elementary school teachers the level of need is so basic, that what a mathematician might envision as an appropriate course is likely to be hopelessly over the heads of most of the students.

• Forget what seems like a good thing to do in some idealized world, and get real: adapt the courses to the actual level and needs of the students.

• The mathematics taught should be connected as directly as possible to the classroom. This is more important, the more abstract and powerful the principles are. Teachers cannot be expected to make the links on their own.

• Get teacher candidates to believe, that mathematics is something you think about - that validity comes from inner conviction that things make sense, that mathematical situations can be reasoned about on the basis of a few basic principles.

• The goal is to have them develop some flexibility in their thinking, to be able to reason about elementary mathematics.

Roger Howe

Adding it Up argues that mathematical proficiency has five strands:

• Conceptual understanding– Comprehension of mathematical concepts,

operations, and relations• Procedural fluency

– Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

mathematical proficiency …

• Strategic competence– Ability to formulate, represent, and solve

mathematical problems• Adaptive reasoning

– Capacity for logical thought, reflection, explanation, and justification

• Productive disposition– Habitual inclination to see mathematics as sensible,

useful, worthwhile, coupled with a belief in diligence and one’s on efficacy.

Educating Teachers of Science, Mathematics, and TechnologyNew Practices for the New

Millennium

A report of the National Research Council’sCommittee on Science and Mathematics

Teacher Preparation

Educating Teachers …argues:1) Many teachers are not adequately prepared to teach science

and mathematics, in ways that bolster student learning and achievement.

2) The preparation of teachers does not meet the needs of the modern classroom.

3) Professional development for teachers may do little to enhance teachers’ content knowledge or the techniques and skills they need to teach science and mathematics effectively.

and recommends:“a new partnership between K-12 schools and the higher education community designed to ensure high-quality teacher education and professional development for teachers.”

The Mathematical Education of Teachers

Is guided by two general themes:

• the intellectual substance in school mathematics; and

• the special nature of the mathematical knowledge needed for teaching.

The MET recommends:• Prospective teachers need mathematics

courses that develop a deep understanding of the mathematics they will teach.

• Prospective elementary grade teachers (K-4) should take at least 9 semester-hours on fundamental ideas of elementary school mathematics.

• Mathematics courses should – focus on a thorough development of basic

mathematical ideas. – develop careful reasoning and mathematical

‘common sense’ in analyzing conceptual relationships and in solving problems.

– develop the habits of mind of a mathematical thinker and demonstrate flexible, interactive styles of teaching.

• The mathematical education of teachers should be based on– partnerships between mathematics and

mathematics education faculty.– collaboration between mathematics faculty

and school mathematics teachers.

The Math Matters Vision• Create a mathematician – mathematics

educator partnership with the goal of improving the mathematics education of future elementary school teachers

• Link field experiences, pedagogy and mathematics instruction

• Create math classes that are both accessible and useful for future elementary school teachers

MATH MATTERS Timeline • Project began 01/01/2000 with NSF support.• AY 2000/2001, first Math Matters cohort (16

students) participated in a year-long, 18-hour block of courses. Each semester had a math class, a pedagogy class, and a field experience.– Significant progress in learning mathematics and in

developing a positive attitude towards teaching math– Significant growth in potential to be an outstanding

teacher– Strong bonding between students and faculty

MATH MATTERS Timeline • Math Matters was repeated with a second cohort

(16 students) during AY2001/2002– Findings similar to first cohort

• AY 2002/2003 – Two experiments with a one-semester, 12 hour block of courses (28 students, 19 students)

• Fall 2003 – The Mathematics Semester begins– Current program is a one-semester, 10-hour, math,

pedagogy, & field experience program.

Barriers to a Successful Partnership

• Math expectations seem to overwhelm students in Elementary Education

• Student evaluations critical of math facultyType of Course Faculty GPA #Students– Honors class 3.20 1,367– All faculty courses 3.04 16,693– Large Lectures 2.88 6,060– Education Majors2.48 726

Comments from a math class for elementary school teachers:

(the course GPA was 2.93)

• This wasn't a course where we learn to teach math. Why do we have to explain our answers.

• I did not like getting a 0 on problems that I attempted. I could have just of left the problem blank then.

• tests are invalid. They ask questions we have never seen before. It would help if we knew more about the questions on the exams - If examples in class were used on the exams.

Comments from a math class for elementary school teachers:

(the course GPA was 2.93)

• Her way of assessing her class aren't fair.

• there was never partial credit. When 20 people drop a class ... there is an obvious problem. [Note: Only 3 of 33 students dropped the class.]

• Test materials were not consistent or reliable with the material covered in class. Grading was very biased.

Comments from a Contemporary Math class

• (She) does a good job making the subject matter interesting. She always seems very enthusiastic about the class and and actual work. More teachers should be like her.

• (She) is a great teacher with a love for her subject that becomes addictive. It has really been my lucky pick to have gotten her as an instructor.

• (She) made the class exciting. It is obvious she enjoys math and teaching. She was always clear in her expectations and directions.

Comments from a Contemporary Math class

• This was a very useful class. I also think that (she) is a great teacher.

• (She) was one of the best teachers I have had here at UNL. She was always available for questions!

• This was a very good class. I failed the class last semester with a different teacher but (she) did a much better job and I am doing great in the class!

Barriers to a Successful Partnership

• Students took math courses before admission to Elementary Education Program

• Math for Elementary Education was often taught by graduate students or part-time lecturers

• Cultural differences in how instruction delivered and students assessed– Fall 2000 Undergraduate GPA by Dept.

• Math 2.53 (UNL’s lowest)• Curr & Inst 3.64 (among highest)

Beliefs of Math and El Ed Faculty1 2 3 4

Strongly Disagree Disagree Agree Strongly Agree El Ed Math Question

• 1.71 2.12 Stated from Traditional Viewpoint------------------------------------------------------------------------------

• 2.00 2.92 Algorithms are best learned through repeated drill and practice.

• 1.57 2.55 An advantage of teaching math is that there is one correct answer.

• 2.00 3.22 Frequent drills on the basic facts are essential in order for children to learn them.

• 1.83 2.70 Time should be spent practicing computational procedures before

children are expected to understand the procedures.

• 2.83 2.14 The use of key words is an effective way for children to solve word problems.

Beliefs of Math and El Ed Faculty1 2 3 4

Strongly Disagree Disagree Agree Strongly Agree

• 3.27 3.07 Stated from Reform Viewpoint ------------------------------------------------------------------------• 3.29 2.25 Teachers should let children work

from their own assumptions when solving problems.

• 3.86 2.78 Mathematics assessment should occur every day.

• 2.71 3.40 Leading a class discussion is one of the most important skills for a math

teacher.

What is the typical ability of a future elementary school teacher at UNL?

How would our students do on two famous problems?

1) How do you solve the problem 1 ¾ / ½ ?Imagine you are teaching division with fractions. Teachers need to write story-problems to show the application of some particular piece of content. What would be a good problem for 1¾/½ ?

• In Knowing and Teaching Elementary Mathematics this question was asked of 23 US teachers. Liping Ma reports:– 9 of 23 US teachers could perform the

calculation using a correct algorithm and provide a complete answer.

– Only 1 of 23 US teachers could create a valid story problem for the computation. It was pedagogically problematic in that the answer involved 3 ½ children.

Surely our teachers and future teachers can do better?

• In the summer of 2002, Ruth interviewed a group of Lincoln Public School teachers who were participating in a summer workshop Jim had organized.

• 14 of 17 (elem and middle level) LPS teachers tested could perform the division of fractions algorithm correctly.

• Only 4 out of 17 could create a valid word problem. – 3 of these 4 were middle school teachers

• We also asked our students to work this problem.Algorithm Word Problem

• Fall 2003 Students 23 of 25 8 of 25• Year 2 (early in sem) 10 of 16 6 of 16• Year 1 (mid year) 12 of 16 10 of 16

Sample solutions from our class last Fall:

Among the better answers we received were these:

• Bobby only ran ½ the distance that he hoped to run in practice. If Bobby ran 1 ¾ miles and that was only ½ of the amount he wanted to run, what was his original goal?

• Bill is running a race that is 1 ¾ miles. The director of the race wants to put markers every ½ mile. How many markers does he need?

Sample solutions from our class this Fall:

Other “solutions” included the following:• Suzie has one and ¾ pies. Ed is hungry and decides he

is going to eat ½ of what Suzie has. When Ed is finished, how many halves of the pie does Suzie have left?

• Jane has 7 quarters. She wants to put the quarters into groups of 2 quarters each. How many groups can she make?

• You have 1 ¾ of a pie! That is not enough. You want ½ more of what they started with. How much more will you need?

• Mom baked 2 pies and divided the pies in quarters. After giving away one slice she’s left with 1 ¾ pies. She then divides each left over piece into halves. How many pieces does she have now?

Perimeter and Area2) A student comes to class

excited. She tells you she has figured out a theory you never told the class. She says she has discovered that as the perimeter of a closed figure increases, the area also increases. She shows you a picture to prove what she is doing.

• The square is 4 by 4– Perimeter = 16– Area = 16

• The rectangle is 4 by 8– Perimeter = 24– Area = 32

• The first day of our Fall 2002 class, we asked our (geometry) students to respond to the area – perimeter question.

• 24 of 32 future elementary teachers believed the child’s theory was correct and indicated that they would congratulate the child.

• Eight of 32 future elementary teachers questioned the child's theory about area and perimeter.

• Only six of the eight explained that the theory was definitely not true.

Mental Math Quiz (Work all problems in your head.)

1) 48 + 39 = 2) 113 – 98 =3) 14 x 5 x 7 = 4) is closest to what integer?5) 4 x 249 = 6) 6(37 + 63) + 18 = 7) .25 x 9 = 8) 12.03 + .4 + 2.36 =9) 1/2 + 1/3 = 10) 90% of 160 =11) The sum of the first ten odd positive integers

(1+3+5+…+17+19) is equal to what integer?12) If you buy items (tax included) at $1.99, $2.99 and

$3.98, the change from a $10 bill would be?13) To the nearest dollar, the sale price of a dress listed at

$49.35 and sold at 25% off is _____?

Mental Math Quiz (Work all problems in your head.)

14) The area of a square of perimeter 20 is ___?15) The ratio of the area of a circle of radius one to that of

a circumscribed square region is closest to? a) .5, b) .6, c) .7, d) .8, e) .9

16) The average (arithmetic mean) of 89, 94, 85, 90, and 97 is _____ ?

17) If 4/6 = 16/x, then x = _____ ?18) If 2x + 3 = 25, then x = _____ ?19) The square root of 75 is closest to what integer?20) To the nearest dollar, a 15% tip on a restaurant bill of

$79.87 is _____ ?

How do UNL’s future elementary school teacher do on the Mental Math Quiz?

• Group Number Median AverageCorrect Correct

• MM Fall 2000 16 15.5 14.8• GW Fall 2003 21 13 13.1• LOK Fall 2003* 19 12 12.7• SW Fall 2003* 23 12 12.4• MM Fall 2001 16 12 12.3• BH Fall 2000 32 12 11.9• JL Fall 2003 24 12 11.8• MM Fall 2002* 28 12 11.6• MG Fall 2001 35 12 11.5• WH Fall 2000 24 11 11.0• WH Fall 2001 32 10 10.9• TM Fall 2003* 20 10.5 10.4• Total 290 12 11.9* LPS Sum Wks. 22 13.5 13.7

* Have already taken the “Arithmetic” course.

The Mathematics Semester(For all Elementary Education majors starting Fall 2003)

MATH• Math 300 – Number and Number Sense (3 cr)

PEDAGOGY• CURR 308 – Math Methods (3 cr)• CURR 351 – The Learner Centered Classroom (2 cr)

FIELD EXPERIENCE• CURR 297b – Professional Practicum Exper. (2 cr)

(at Roper Elementary School)– Students are in Roper Elementary School on Mondays and

Wednesdays (four hours/day)– Math 300 & CURR 308 are taught as a 3-hour block on Tuesday

and Thursday– CURR 351 meets at Roper on Wednesdays

A look inside Math Matters(and The Mathematics Semester)

• Early math assignments establish our expectations• Professional/Reflective Writings• Curriculum Materials• Number and Number Sense Items• Working together as a team• The Curriculum Project• Some Geometry Assignments• Activities at Roper

– Teaching a Math Lesson– Child Study

• Learning and Teaching Project





Fall 2001 – The Rice Problem • (This assignment builds on a N&NS problem.) Recall our

discussion about the game of chess and how a humble servant for a generous king invented it. The king became fascinated by the game and offered the servant gold or jewels in payment, but the servant replied that he only wanted rice—one grain for the first square of the chess board, two on the second, four on the third, and so on with each square receiving twice as much as the previous square. In class we discussed how the total amount of rice was 264 grains of rice. (To be completely precise, it is this number minus one grains of rice.) Suppose it was your job to pick up the rice. What might you use to collect the rice, a grocery sack, a wheelbarrow, or perhaps a Mac truck? Where might you store the rice?

Fall 2001 – A letter from 1st & 2nd graders Dear Math Professors,

We are 1st and 2nd graders in Wheeler Central Public School in Erickson, Nebraska. We love to work with big numbers and have been doing it all year! Every time we read something with a big number in it we try to write it. Then our teacher explains how to write it. We are getting pretty good at writing millions and billions!

We have a problem that we need your help with. We were reading amazing ‘Super Mom’ facts in a Kid City magazine. It told how many eggs some animals could lay. We came across a number that we don’t know. It had a 2 and then a 1 followed by 105 zeros!! We wrote the number out and it stretches clear across our classroom! We know about a googol. We looked it up in the dictionary. A googol has 100 zeros. Then what do you call a number if it has more than 100 zeros? Is there a name for it?

Another problem is that we learned about using commas in large numbers. In the magazine article they used no commas when writing this large number. That confused us. Also, if you write a ‘googol’ with 100 zeros, how do you put the commas in? It doesn’t divide evenly into groups of 3 zeros. There will be one left over.

We appreciate any help you can give us solving this “big” problem. Thank you for your time.

Sincerely,

Mrs. Thompson’s 1st & 2nd gradersMegan Kansier, Mark Rogers Marcus Witt, Ashley Johnson

clipping from Kid City magazineApple Of My EyeThe tiny female apple aphid is a champ as an egg-layer. This insect can lay as many as 21000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 eggs in 10 months.

Fall 2003 – Making change What is the fewest number of coins that it will take to make 43 cents if you have available pennies, nickels, dimes, and quarters? After you have solved this problem, provide an explanation that proves that your answer is correct?

How does the answer (and the justification) change if you only have pennies, dimes, and quarters available?





Professional/Reflective Writings

Purpose: To make connections within and across mathematical, pedagogical, and field experiences through writing.

Professional/Reflective WritingsRead “What do Math Teachers Need to Be?” The author is Herb Clemens, a mathematics professor at The University of Utah, and the article was published in 1991 in Teaching academic subjects to diverse learners (pp. 84-96). In this article, Herb Clemens lists what he thinks teachers of mathematics need to be. After reading his article and his meaning and use of these words, where does your own practice of teaching mathematics stand in relationship to what Clemens says mathematics teachers need to be: unafraid, reverent, humble, opportunistic, versatile, and in control of their math. On p. 92, Clemens lists four fundamental questions about mathematics teaching that matter to him. If he came to your practicum classroom and watched you teach a math lesson tomorrow, how would he answer his own last question about your practice: Can this teacher teach it [math] with conviction, and with some feeling for its essence? Explain.

Professional/Reflective WritingsSome educators argue that there is real value in teaching children mathematics in diverse, heterogeneous classrooms. Some teachers may counter this position, contending that it is best for children if students are homogeneously grouped for mathematics instruction. Pick a position in this argument and articulate it in writing. State your position and explain why you believe what you do. Your reasons for believing what you do may come from past teaching and learning experiences (your own and others’), and things that you’ve read, or learned in other courses.

Professional/Reflective WritingsRead "Teaching While Leading a Whole-Class Discussion," Chapter 7 from Lampert’s book. In this chapter Lampert examines problems of practice that arise while addressing a whole group of students or choosing students to answer questions. As you read the chapter find places in the chapter where you can relate Lampert's writing to your own experiences in the practicum setting while teaching math and maybe even other subjects. Use quotes from the text that connect to your experiences. Explain how and why they relate.





Curriculum Materials

Adapting NSF funded curriculum materials:• Schifter, D., Bastable, V., & Russel, S.J. (1999).

Number and operations, part I: Building a system of tens. Parsippany, NJ: Dale Seymour.

• Schifter, D., Bastable, V., & Russel, S.J. (2001). Geometry: Examining features of shape. Parsippany, NJ: Dale Seymour.

• Sowder, J. et al. (2000). Number and number sense. San Diego State University. Shapes and measurement. San Diego State University.

Curriculum Materials

Other materials used:• Ladsen-Billings, G. (1997). The dreamkeepers:

successful teachers of African American children. Sanfrancisco: Jossey-Bass.

• Lampert, M. (2001). Teaching problems and the problems of teaching. New Haven, CT: Yale University.

• Charney, R. (1992). Teaching children to care. Greenfield, MA: Northeast Foundation for Children.

• Reys, R., Lindquist, M., Lambdin, D.V., Smith, N.V., & Suydam, M.N. (2003). Helping children learn mathematics. NY: John Wiley & Sons, Inc.





A Typical Weekly Homework All Shook Up

Five couples met one evening at a local restaurant for dinner. Alicia and her husband Samuel arrived first. As the others came in some shook hands and some did not. No one shook hands with his or her own spouse. At the end Alicia noted that each of the other 9 people had shaken the hands of a different number of people. That is, one shook no one's hand, one shook one, one shook two, etc., all the way to one who shook hands with 8 of the people. How many people did Samuel shake hands with?

Sample Test Items

1) Give an example of one number that you are sure is an irrational number. Explain why you know that it is irrational.

2) Let B = 11232. Factor B into a product of powers of prime numbers. Then factor B2 into a product of powers of prime numbers.

3) What is the smallest positive integer with exactly 10 factors?

4) Is 250 a factor of 10030? Explain.

Is 250 a factor of 10030? Explain.

8.881784197 E44

Is 250 a factor of 10030? Explain.

8.881784197 E44

30 30 30 60 6010 60

50 50 50

100 4 *25 2 *5 2 *52 2 2





"Why is this stuff so hard?" I believe this test, this class, this subject, are all difficult because they involve thinking in different ways than what we are used to. We have all been conditioned, in our own education; to believe that things are the way they are, and that's all there is to it. We haven't challenged ideas and proofs nearly as much as we should have. Asking "Why" to an idea or trying to understand the reasoning behind something is just not something most of us are used to doing. That's why this stuff is hard.

Miss A

"Why is this stuff so hard?"

I don't have a difficult time with abstract ideas. I love it when we work with new concepts. … I just want you to know that I have almost always been able to figure math problems out and I get VERY frustrated when I get stumped. I am very stubborn like that. Please don't take my temper personally.

Miss J

"Why is this stuff so hard?"

The major problem that I had was my reasoning for the factoring problem. I started off thinking that I should try dividing 2^50 into 100^30, but the large numbers were daunting, so I panicked and tried using my calculator. The answer it gave me did not look pretty, which I think is what triggered my fall down a road of insanity (see my test for more details). Bad, bad calculators ....once you started to explain the problem on the board, I wanted to smack myself in the head for being so silly. Miss P





Curriculum ProjectThe goal is to investigate a new mathematical area of the elementary curriculum and consider what teachers need to know as well as what children need to learn the topic in the deep and meaningful ways suggested by the NCTM Standards (2000).

1) Pick a topic: data analysis and probability, geometry, reasoning and proof, or algebra.

2) Read, analyze, and synthesize the mathematical topic in the NCTM Standards.

3) Analyze and synthesize the topic in a set of reform curriculum materials (Everyday Math, Trail Blazers, Investigations, local curriculum).

4) What do teachers need to know to teach this?5) Create 5 math problems that would help teachers learn. Create 5

math problems that would help children learn.





Geometry ProblemsA) How many different squares are there on a checkerboard? If the

number of rows and columns of the checkerboard is doubled, how does the number of squares change?

B) Let “T” be the lower left-hand corner of a checkerboard and let “B” be the intersection of the 6th vertical line and the 5th horizontal line counting from the lower left-hand corner. Suppose you want to move from T to B and all movement must be horizontal or vertical along lines formed by the various squares on the checkerboard. The shortest path has length “11” in terms of a unit equal to a side of a small square. How many different paths have length 11? Can you prove it?

C) Consider a large circle and pick “n” points on the circle. [Here n might be 2, 3, 4, and so forth.] Connect each pair of points with a chord. Notice that if n = 2 the circle is cut into 2 regions. If n = 3 the circle is cut into 4 regions and if n = 4 the circle is cut into 8 regions. How many regions do you get if n = 6? What about n = 8?





Math Lesson #1

You need to teach a math lesson. It should connect to the curriculum in the classroom in which you are working. You should make use of the textbook and other resources from your cooperating teacher and what you are learning and reading in your courses with Jim and Ruth this semester.

Child Study

This assignment will give you some experience watching, listening to, probing, and assessing one child’s understanding of several math problems focused on a particular area of mathematics. You will write a report of your interview and suggest instruction for the child based on the information you gathered in the interview session.





Learning and Teaching Project Area and Perimeter

The task began with a homework problem. It is taken from Reconceptualizing Mathematics: Courseware for Elementary and Middle School Teachers, Center for Research in Mathematics and Science Education, 1998.

Is there a relationship between the area and the perimeter of a polygonal shape made with congruent square regions? (For fixed area, find the minimum and maximum perimeter. For fixed perimeter, find the minimum and maximum area.) Squares must be joined complete-side to complete-side. The outside “boundary” should be a polygon. In particular, this would not permit a shape with a “hole” in the middle.

A couple of weeks later we told our students:

We want to revisit the “Area and Perimeter” problem. This is to be the basis for a mathematics lesson that you will videotape yourself teaching to one elementary school student.

How can you present this task to the student you will teach? How can you set the stage for the student to understand the problem? How far can the student go in exploring this problem? Remember that you want your student to discover as much as possible for himself (or herself). But there may be some critical points where you need to guide the student over an intellectual “bump” so that he (she) can move on to the next part of the problem.

Finally, produce a report analyzing the mathematics and your teaching experience.

Shapes from Four Triangles

The task began with a problem on a midterm exam. It is taken from Reconceptualizing Mathematics: Courseware for Elementary and Middle School Teachers, Center for Research in Mathematics and Science Education, 1998.

Given four congruent isosceles right triangles, how many different polygonal regions can you make, using all four triangles each time?

Several weeks later we told our students:

We want to revisit the “Shapes from Four Triangles” problem. This is to be both a mathematical task for you and the basis for a mathematics lesson that you will teach to one elementary school student.

How many different polygonal regions can be made using all four isosceles right triangles each time? How do you give a mathematical argument that you have found a complete set of shapes and that you have no duplications?

How can you present this task to the student you will teach? How can you set the stage for the student to understand the problem? How far can the student go in exploring this problem?

Remember that you want your student to discover as much as possible for himself (or herself). But there may be some critical points where you need to guide the student over an intellectual “bump” so that he (she) can move on to the next part of the problem.

Is Math Matters a Success?

• The response from students has been positive. • Students are engaged in research projects

– Each year several students have sought to participate in a 1- 2 year research project funded by UNL’s UCARE program or NSF-REU funds

• Yr 1 – 4 students• Yr 2 – 4 students• Yr 3 – 4 students• Yr 4 – 2 students

• The project evaluator reports:– significant cohesion among the students; a

community of professionals with high standards– Cooperating teachers working with the elementary

teacher education program assess current or former MM students as better prepared to be a teacher than a control group at a comparable point in their teacher education program.

• MM graduates are finding jobs. Several indicate their preparation to be an outstanding math teacher was key to their successful job search.

Comparison of Math Matters Students to Other Students in Scale Scores

1 2 3 4 5

Planning*

Reform Instruction

Traditional Instruction

Assessment

Responsiveness to Students

Math Content*

Problem Solving

Mean Frequency in Percent of Time (1=0%, 2=25%, 3=50%, 4=75%, 5=100%)*significant difference (p<.05)

Others (n=56-75)Math Matters (n=14-16)

Comparison of Math Matters Students to Other Students in Preparedness to Teach

1 2 3 4

create meaningful lessons*

meet diverse needs of students

manage hands-on activities*

facilitate student discussion*

help students develop own problem solving*

encourage cooperative learning*

apply own understanding of math concepts*

use a variety of assessment*

Level of Preparedness (1=not adequately, 2=somewhat, 3=fairly well, 4=very well)*significant difference (p<.05)

Others (n=74-78)Math Matters (n=16)

Comparison of Math Matters Students to Other Students in Preparedness to Teach

1 2 3 4

mathematics*

reading/language arts

science

social studies

art

Level of Preparedness (1=not adequately, 2=somewhat, 3=fairly well, 4=very well)*significant difference (p<.05)

Others (n=51-77)Math Matters (n=14-16)

What are we learning?

• Integrate content and pedagogy course offerings.

• Keep expectations of students high.• Emphasize learning how to learn and offer

continued opportunities.

• Build on existing relationships.• Commitment to the partnership need to be

long term.• Partnership relationships need to extend

beyond the relationship of two individuals.

What do we want to learn from our teacher education efforts?

• What happens to our students when they leave our project and start teaching in their first jobs?

• How do our former students use (or do they use) the mathematical knowledge they learned in teacher education for teaching? What kinds of challenges do they face?

• What are these new teachers’ abilities to– Choose and use mathematical

representations?– Give and evaluate mathematical

explanations?– Choose and use precise mathematical

definitions?

(Ball, Lubienski, and Mewborn, 2001, Handbook of Research on Teaching)

A visit to Carla’s 1st Grade Class

• “Carla” was in our first cohort of “Math Matters” students. She volunteered for the program because she considered herself weak in mathematics and she was highly motivated to be a good teacher.

• This Spring, Dr. Heaton and I visited Carla’s 1st Grade Class. The school was located in a “low-income” area of Lincoln.

Carla was teaching a geometry lesson

• The lesson was masterfully crafted. Time was used efficiently. For over an hour the students were eagerly engaged in learning mathematics. Carla’s explanations were clear and her use of terminology was careful. Most importantly, the classroom was filled with questions: – Why?– How do you know?– What does that mean? etc.

• There was lots of encouragement and plenty of praise for a job well done. One comment stood out. Repeatedly, these 1st grade students were rewarded with the encouragement:

You are so smart!That’s why you are mathematicians!