Text:  Mathematics for Elementary School Teachers, A Contemporary Approach,   4th Edition  by  Gary L. Musser and William F. Burger  (available at K-State Union Book Store).

Class Attendance: Students are  required to attend class and participate in classroom activities on a regular basis.  Student participation in classroom activities is an important part of  the learning process. Students' attendance will  be checked in a random manner.

Course Objectives:   First of all, this course is a content area course in teacher education.  Students will have a course in the College of Education  concentrating on methods of teaching mathematics. Thus this course will concentrate on  teaching the teachers to understand mathematical materials although it will be emphasized throughout the semester how the material should be taught in elementary schools.  Students are strongly encouraged to review the  Kansas Teacher Licensure Standards (KTLS),  NCATE Standards,  and Kansas Mathematics  Curricular Standards for K-12  (KMCS)  and Kansas teacher certification standards for Late Childhood through Early Adolescent License Level  (LCEALL)   (See the attachments).

As indicated in the standards, it is important that future teachers not only understand the basic concepts of the content areas they are going to teach, but also be able to explain to their students, in different ways,  the concepts and  be able to relate  concepts to students' experience to facilitate  students' learning experience and to stimulate students' problem solving ability.

In this course I will make efforts to:

1. emphasize  thinking and reasoning instead of simply asking students to memorize formulas,
2. look at some of the materials you may have learned before from a  different angle;
3. discover and prevent "popular"  mistakes, you and/or your  students might make;
4. bring the mathematics down to a more enjoyable level for you and your future students using examples from daily life, which will help you to  understand the subject.
5. help students to understand the development of mathematical concepts over history, which helps teachers get the experience of "putting themselves in the position of elementary school students.

A. Classroom Participation. Since each of the concepts covered in the course have been seen by students earlier and students are preparing themselves to teach,  students should practice their reading skills by reading each section of the textbook before class. While reading the textbook, students should keep in mind the follow questions and write a reading card to be turned in.

1. Do you understand the exposition? Provide a list of unclear concepts or parts you don't understand.
2. What is the difference between the materials presented here in the textbook and  those you learned in school?
3. How can you relate each of the mathematical concepts and algorithms to daily life examples? Give a list of those you don't how to relate.

B. Homework. Working through problems will aid in further understanding of the concepts and materials. Homework will be assigned periodically.  Each assignment will consist of two sets of problems.  One set is homework, which students must  do completely  and turn in by the due date to be graded.  Another set consists of practice problems, which all students should try to do, though it is not required they they be turned in and graded.  However,  exams will  cover these practice problems.

C. Studying Group.  Discussions. It is an important part of the teaching experience that teachers work in groups to prepare teachering materials and to discuss teaching strategies. Periodically, there will be discussion of topics assigned to discussion groups.  Each member of the group should actively participate. Groups will be randomly asked to present their findings in class.  A random member will be asked to represent the group's results. The group's grade will be determined by the presentation of the randomly  chosen presenter. It is important that everyone in the group be able to present the group's findings.

D. Review Cards and Exams. Periodically reviewing and reorganizing learned material is just like harvesting the crops from the field after many months of hard work.  Exams provide such an opportunity  to review and master the materials. Students will be required to write their own review sheets  of limited size, which should be turned in right before the exam. Students' review sheets will be graded based on how they organize the materials and choose major concepts.

E. Project and Report. Each student should try to find a child of at most seven year old to explain to the child a certain concept.  They could plan to work with  a daycare center or as a school helper, and then write  a report outlining

1. The child's background--  things the child likes to do.
2. The plan you you made to teach the child the concept.
3. The procedure you actually carried out your plan.
4. The child's reaction (Did the child have any difficulty of understanding the concept? How did you know?)
5. The outcome of the child's learning (Did the child eventually understand the concept?  How did you know that that the child understood?)
6. Summary your experience. If your are going to do this with a second,  do you think you can do better?  How to improve?

 

Each portion of the contribution will be converted to percentage average before it is used for overall computation using the above mentioned weighting system.

To convert to letter grades for the course from Overall Score:
 

Overall	89 or higher	between 77 and 89	between 63 and 77	between 50 and 63	below 50
Letter Grade	A	B	C	D	F

 
 

Midterm Exam Wed. Oct 18. in Class
Group Project I:  Due Monday, Oct. 27

 Students should form groups of size from 2-4 to work together and each group should write a report include the following:

(1). Write down the meaning of base eight numbers with an emphasis in place values and an instruction on how to convert numbers from base ten to base eight and vice verse.

(2). Write down the addition table in base eight  and write an instruction supported with examples show how to do addition using standard algorithm of multi-digit numbers as as one does in base ten. The instruction should be able to be understood by third graders.

(3). Use the additon table, write an instruction how to perform simple subtraction and  multidigit number subtractions using the standard algorithm support with examples.

(4).  Do the same as in (2) but for multiplication.

(5). Do the same as in (3) but for division.

(1). Design the game for your students to play.
(2). Write an argument using the divisibility test in Chapter 5 and the expanded notitions of numbers to explain to your students why the answer is always 9.
(3). In your report. you need to state how you are going to play this game with your students and How do you plan to convince your students that your argument in  they understand.
 

 
Individula Project: Due on Friday Dec. 1
Try to work a child of age at most 8 to teach the child the concept of negative numbers. Write a report of your project. Your report should contain the following:

1. The child's background--  things the child likes to do.
2. The plan you you made to teach the child the concept.
3. The procedure you actually carried out your plan.
4. The child's reaction (Did the child have any difficulty of understanding the concept? How did you know?)
5. The outcome of the child's learning (Did the child eventually understand the concept?  How did you know that that the child understood?)
6. Summary your experience. If your are going to do this with a second,  do you think you can do better?  How to improve?

 

PROFESSIONAL EDUCATION OUTCOMES

  ......

OUTCOME #2 The educator demonstrates the ability to integrate curriculum across and within
subject areas in such a way as to facilitate the students' abilities to understand relationships
within the content fields.

Knowledge

1.The educator can relate disciplinary knowledge to other subject areas and to student life
     experiences.

Disposition

  1.The educator demonstrates enthusiasm for each discipline he or she teaches and actively promotes
     connections between classroom subject matter and everyday life.
  2.The educator recognizes contributions of other disciplines and assists students in seeing
     relationships and connections among disciplines.
  3.The educator values planning as a collegial activity.
  4.The educator recognizes the value of students’ prior learning and experiences.

Performance

  1.The educator creates interdisciplinary learning experiences that allow students to integrate
     knowledge, skills, and methods of inquiry from several subject areas.
  2.The educator effectively uses multiple representations and explanations to help students construct
     new knowledge by building on prior student understandings.
  3.As an individual and a member of a team, the educator selects and creates integrated learning
     experiences that are appropriate for curriculum goals, relevant to learners, and based upon
     principles of effective instruction.
  4.The educator participates in collegial activities designed to integrate curricula across subject areas.

OUTCOME #3 The educator demonstrates the central concepts, tools of inquiry, and structures
of each discipline he or she teaches and can create opportunities, including integrated learning
experiences, that make these aspects of subject matter meaningful for students.

Knowledge

(detailed standards for discipline-based knowledge are included in the content endorsement
outcomes.)

  1.The educator understands major concepts, assumptions, debates, processes of inquiry, and ways of
     knowing that are central to the discipline she or he teaches.
  2.The educator understands that students’ conceptual frameworks and their misconceptions for an
     area of knowledge can influence their learning.

Disposition

  1.The educator realizes that subject matter knowledge is not a fixed body of facts but is complex and
     ever-evolving. The teacher seeks to keep abreast of new ideas and understandings in professional
     education and subject matter.
  2.The educator appreciates that students learn in different ways and guides students in constructing
     their own knowledge.
  3.The educator is committed to continual learning and engages in professional discourse about
     subject matter knowledge and student’s learning of the discipline.

Performance

  1.The educator represents and uses differing viewpoints, theories, “ways of knowing,” and methods
     of inquiry in his or her teaching of subject matter concepts.
  2.The educator evaluates teaching resources and curriculum materials for their comprehensiveness,
     accuracy, and usefulness for representing particular ideas and concepts.
  3.The educator engages students in constructing knowledge and testing hypotheses according to the
     methods of inquiry and standards of evidence used in the discipline.
  4.The educator develops or adapts and uses curricula that encourage students to see, question, and
     interpret ideas from diverse perspectives.
 
 

....
2d. Mathematics--Candidates know, understand, and use the major concepts, procedures, and reasoning processes of mathematics that define number systems and number sense, geometry, measurement, statistics and probability, and algebra in order to foster student understanding and use of patterns, quantities, and spatial relationships that can represent phenomena, solve problems, and manage data;

Supporting explanation

Candidates are able to teach elementary students to explore, conjecture, and reason logically using various methods of proof; to solve non-routine problems; to communicate about and through mathematics by writing and orally using everyday language and mathematical language, including symbols; to represent mathematical situations and relationships; and to connect ideas within mathematics and between mathematics and other intellectual activity. They help students understand and use measurement systems (including time, money,temperature, two and three dimensional objects using non-standard and standard customary and metric units); explore pre-numeration concepts, whole numbers, fractions, decimals, percents and their relationships; apply the four basic operations (addition, subtraction, multiplication, and division) with symbols and variables to solve problems and to model, explain, and develop computational algorithms; use geometric concepts and relationships to describe and model mathematical ideas and real-world constructs; as well as formulate questions, and collect, organize, represent, analyze, and interpret data by use of tables, graphs, and charts. They also help elementary students identify and apply number sequences and proportional reasoning, predict outcomes and conduct experiments to test predictions in real-world situations; compute fluently; make estimations and check the reasonableness of results; select and use appropriate problem-solving tools, including mental arithmetic, pencil-and-paper computation, a variety of manipulatives and visual materials, calculators, computers, electronic information resources, and a variety of other appropriate technologies to support the learning of mathematics. Candidates know and are able to help students understand the history of mathematics and contributions of diverse cultures to that history. They know what mathematical preconceptions, misconceptions, and error patterns to look for in elementary student work as a basis to improve understanding and construct appropriate learning experiences and assessments.

Source documents for mathematics

Professional Standards for Teaching Mathematics, National Council of Teachers of Mathematics, 1991
Curriculum and Evaluation Standards for School Mathematics, NCTM, 1989
Principles and Standards 2000 for School Mathematics, NCTM, (forthcoming, April 2000)
Assessment Standards for School Mathematics, NCTM, 1995
NCATE Program Standards, "Programs for Initial Preparation of Teachers of Mathematics, prepared by the National Council of Teachers of Mathematics, approved by the National Council for Accreditation of Teacher Education, 1998
 
 

OUTCOME #6 The teacher of late childhood through early adolescent demonstrates the need for, uses of, and
relationships in number systems and number theory from both an abstract and concrete perspective and are able to
identify real world applications.

Knowledge

The teacher understands:

  1.number sense, including a sense of magnitude, mental mathematics, estimation, place value, multiple representations of
    numbers, convergence, infinity, and a sense of the reasonableness of results.
  2.properties of numbers, including place value, primes, factors, multiples, inverses, and the extension of the these concepts
    throughout mathematics.
  3.the use of numbers to quantify and describe phenomena such as time, temperature, money, and trends.
  4.number systems, their properties, operations, ordering, and relations, including the natural numbers, whole numbers,
    integers, rational numbers, irrational numbers, real numbers, and complex numbers.
  5.computational procedures, including common and uncommon algorithms; mental strategies; use of manipulatives and
    other representations; paper and pencil; and technology and the role of each.
  6.the use of fractions, decimals, ratio, proportion, and percent to represent and solve problem situations within and outside
    of mathematics.

Disposition

The teacher:

  1.demonstrates a positive attitude about number systems and number theory.
  2.demonstrates confidence in his/her ability to apply number concepts.
  3.demonstrates enthusiasm for the teaching of number concepts.
  4.demonstrates an understanding of the role of number systems as a part of the coherent structure of mathematics.
  5.values number systems and their applications.
  6.promotes students' confidence, flexibility, perseverance, curiosity, and inventiveness in using number systems through
    the selection of appropriate tasks and by engaging students in mathematical discourse.

Performance

The teacher will:

1. investigate, formulate, and solve problems using different strategies, verify and interpret results, and generalize solutions.

2. explore mathematical questions and conjectures, formulate counterexamples, construct and evaluate arguments using
intuitive, informal exploration and proof.

3. express mathematical ideas orally, in writing, and visually using the power of mathematical language, notation, and
symbolism.

4. demonstrate the interconnectedness of the concepts and procedures of mathematics and makes connections among other
disciplines and real world mathematics.

5. encourage students to explore, select and use appropriate tools from technology and/or concrete materials to model
mathematical ideas.

6. apply knowledge of the historical bases of mathematics and the problems societies faced that gave rise to mathematical
systems, acknowledging the contributions made by individuals, of various cultures in ancient and modern mathematics.

OUTCOME #7 The teacher of late childhood through early adolescent demonstrates the need for, uses of, and
relationships in geometry, measurement, and spatial sense from both an abstract and concrete perspective and are able
to identify real world applications.

Knowledge

1. Shapes and the ways in which they can be derived and described in terms of dimension, direction, orientation, similarity,
congruence, perspective, and the relationships among these properties.

2. Spatial sense, symmetry, and the ways in which shapes can be visualized, combined, subdivided, and changed to illustrate
concepts, properties, and relationships.

3. Use of both oral and written communication to describe relationships among geometric concepts including symmetry,
congruence, and similarity.

4. Spatial reasoning and the use of geometric models to represent, visualize, and solve real-world and mathematical problems.

5. Motion and the ways in which rotation, reflection, and translation of shapes can illustrate concepts, properties, and
relationships.

6. Analysis of two- and three- dimensional figures including tessellations, polygons, polyhedra, and curved shapes.

7. Attributes of shapes and objects that can be measured, including length, area, volume, capacity, size of angles, weight, and
 mass.

8. The structure of systems of measurement, including the development and use of measurement systems and the relationships
within and across different systems.

9. Estimation and/or measurement of a quantity in metric or customary units including but not limited to time, money, length,
angle, area, volume, mass, capacity, and temperature using the appropriate measuring instrument.

10. Indirect measurement, and its uses, including developing formulas and procedures for determining measures to solve
problems.

11. Formal and informal argument, including the processes of: making assumptions, formulating, testing, and reformulating
conjectures; and justifying arguments based on geometric figures.

Disposition

The teacher:

  1.demonstrates a positive attitude about geometry.
  2.demonstrates confidence in his/her ability in geometry.
  3.demonstrates enthusiasm for the teaching of geometry.
  4.demonstrates an understanding of the role of geometry as a part of the coherent structure of mathematics.
  5.values geometry as a mathematical tool and its application in other disciplines and in society.
  6.promotes students' confidence, flexibility, perseverance, curiosity, and inventiveness in doing geometry through the use
    of appropriate tasks and by engaging students in mathematical discourse.

Performance

The teacher will:

1. investigate, formulate, and solve problems using different strategies, verify and interpret results, and generalize solutions.

2. explore mathematical questions and conjectures, formulate counterexamples, construct and evaluate arguments using
intuitive, and informal exploration.

3. express mathematical ideas orally, in writing, and visually using the power of mathematical language, notation, and
symbolism.

4. demonstrate the interconnectedness of the concepts and procedures of mathematics and makes connections among other
disciplines and real world mathematics.

5. encourage students to explore, select and use appropriate tools from technology and/or concrete materials to model
mathematical ideas.

6. apply knowledge of the historical bases of mathematics and the problems societies faced that gave rise to mathematical
systems, acknowledging the contributions made by individuals, of various cultures in ancient and modern mathematics.
 

OUTCOME #8 The teacher of late childhood through early adolescent demonstrates the need for, uses of, and
relationships in statistics and probability from both an abstract and concrete perspective and are able to identify real
world applications. The use of appropriate technology is essential.

Knowledge

The teacher understands:

1. Investigations using data; including formulating a problem, devising a plan to collect data, and systematically collecting,
recording and organizing data.

2. Data representation to describe data distributions and central tendency through appropriate use of graphs such as bar graphs,
line graphs, circle graphs, pictographs, histograms, as well as line plots, stem and leaf plots, scatter plots, and box plots.

3. Data representation to describe data distributions and central tendency through appropriate use of tables and summary
statistics such as mean, median, mode, variance, standard deviation, and percentile rankings.

4. Analysis and interpretation of data, making both verbal and written inferences and interpretations, using these in real world
problems to predict outcomes, making recommendations or decisions, and creating or evaluating arguments and results.

5. Inference, and the role of randomness and sampling in statistical claims about populations.

6. Probability as a way to describe chance or risk in simple and compound events such as in a description of a fair game, odds,
and coincidence.

7. Prediction of outcomes and decision making based on exploration of probability through data collections, experiments, and
simulations using two sided counter, number cubes, spinners, random numbers, and computer/calculator programs.

8. Prediction of outcomes based on theoretical probabilities, and comparison of mathematical expectations with experimental
results.

9. Recognition of potential misuses of statistics and common misconceptions about probability.

10. Finding the line of best fit given a set of data.

Disposition

The teacher:

  1.demonstrates a positive attitude about statistics and probability.
  2.demonstrates confidence in his/her ability in statistics and probability.
  3.demonstrates enthusiasm for the teaching of statistics and probability.
  4.demonstrates an understanding of the role of statistics and probability as a part of the coherent structure of mathematics.
  5.value statistics and probability as mathematical tools and their applications in other disciplines and in society.
  6.promote students' confidence, flexibility, perseverance, curiosity, and inventiveness in using statistics and probability
    through the use of appropriate tasks and by engaging students in mathematical discourse.

Performance

The teacher will:

1. investigate, formulate, and solve problems using different strategies, verify and interpret results, and generalize solutions.

2. explore mathematical questions and conjectures, formulate counterexamples, construct and evaluate arguments using
intuitive, and informal exploration.

3. express mathematical ideas orally, in writing, and visually using the power of mathematical language, notation, and
symbolism.

4. demonstrate the interconnectedness of the concepts and procedures of mathematics and makes connections among other
disciplines and real world mathematics.

5. encourage students to explore, select and use appropriate tools from technology and/or concrete materials to model
mathematical ideas.

6. apply knowledge of the historical bases of mathematics and the problems societies faced that gave rise to mathematical
systems, acknowledging the contributions made by individuals, of various cultures in ancient and modern mathematics.

OUTCOME #9 The teacher of late childhood through early adolescent demonstrates the need for, uses of, and
relationships in patterns, functions, and algebra from both an abstract and concrete perspective and are able to
identify real world applications.

Knowledge

The teacher understands:

1. Patterns, including an ability to recognize, describe, analyze, extend, and create a wide variety of patterns.

2. Functions, continuous and discrete, and their use to describe relations and to model a variety of real world situations.

3. Representations of situations and solutions of problems that involve variable quantities with expressions, equations, and
inequalities, including algebraic, geometric and combinatorial relationships.

4. Multiple representations of relations by tables, graphs, words, and symbols, the strengths and limitations of each
representation, and conversion from one representation to another, using appropriate graphing technology.

5. Attributes of polynomial, rational, algebraic, and exponential functions.

6. Modeling to solve problems, to understand and describe the behavior of a system or event, and to predict its behavior based
on past experiences.

Disposition

The teacher:

  1.demonstrates a positive attitude about algebraic concepts.
  2.demonstrates confidence in his/her ability in algebraic concepts.
  3.demonstrates enthusiasm for the teaching of algebraic concepts.
  4.demonstrates an understanding of the role of algebraic concepts as a part of the coherent structure of mathematics.
  5.values algebraic concepts as mathematical tools and their applications in other disciplines and in society.
  6.promotes students' confidence, flexibility, perseverance, curiosity, and inventiveness in using algebraic concepts through
    the use of appropriate tasks and by engaging students in mathematical discourse.

Performance

The teacher will:

1. investigate, formulate, and solve problems using different strategies, verify and interpret results, and generalize solutions.

2. explore mathematical questions and conjectures, formulate counterexamples, construct and evaluate arguments using
intuitive, and informal exploration.

3. express mathematical ideas orally, in writing, and visually using the power of mathematical language, notation, and
symbolism.

4. demonstrate the interconnectedness of the concepts and procedures of mathematics and makes connections among other
disciplines and real world mathematics.

5. encourage students to explore, select and use appropriate tools from technology and/or concrete materials to model
mathematical ideas.

6. apply knowledge of the historical bases of mathematics and the problems societies faced that gave rise to mathematical
systems, acknowledging the contributions made by individuals, of various cultures in ancient and modern mathematics.

OUTCOME #10 The teacher of late childhood through early adolescent demonstrates the need for, uses of, and
relationships in discrete processes from both an abstract and concrete perspective and are able to identify real world
applications.

Knowledge

The teacher understands:

1. Counting techniques (including combinations and permutations) and their use in collecting and organizing information, and
solving problems.

2. Representation and analysis of discrete mathematics problems, including basic concepts of sequences, graph theory, arrays,
Venn diagrams, and networks.

3. Generation of patterns using iteration and recursion.

Disposition

The teacher:

  1.demonstrates a positive attitude about discrete mathematics.
  2.demonstrates confidence in his/her ability in discrete mathematics.
  3.demonstrates enthusiasm for the teaching of discrete mathematics.
  4.demonstrates an understanding of the role of discrete mathematics as a part of the coherent structure of mathematics.
  5.values discrete mathematics as a mathematical tool and its application in other disciplines and in society.
  6.promotes students' confidence, flexibility, perseverance, curiosity, and inventiveness in using discrete mathematics
    through the use of appropriate tasks and by engaging students in mathematical discourse.

Performance

The teacher will:

1. investigate, formulate, and solve problems using different strategies, verify and interpret results, and generalize solutions.

2. explore mathematical questions and conjectures, formulate counterexamples, construct and evaluate arguments using
intuitive, and informal exploration.

3. express mathematical ideas orally, in writing, and visually using the power of mathematical language, notation, and
symbolism

4. demonstrate the interconnectedness of the concepts and procedures of mathematics and makes connections among other
disciplines and real world mathematics.

5. encourage students to explore, select and use appropriate tools from technology and/or concrete materials to model
mathematical ideas.

6. apply knowledge of the historical bases of mathematics and the problems societies faced that gave rise to mathematical
systems, acknowledging the contributions made by individuals, of various cultures in ancient and modern mathematics.

OUTCOME #11 The teacher of late childhood through early adolescent demonstrates the ability to use and teach the
science process skills necessary to do scientific inquiry and problem solving.

Knowledge

The teacher understands:

1. how to plan and conduct authentic research using the process skills.

2. how to design science activities, using the science process skills, to teach developmentally appropriate science content.

Disposition

1. The teacher appreciates the importance of the process skills as a means of learning science concepts.

2. The teacher values the process skills as a means of solving problems.

3. The teacher believes that all students have the opportunity to attain a high level of scientific literacy.

4. The teacher values truth, objectivity, open mindedness, creativity, intellectual curiosity, discovery and responsible reporting
when using the processes of science.

Performance

1. The teacher selects real life problems for students to investigate.

2. The teacher facilitates student planned and conducted investigations.

3. The teacher provides the opportunity for students' discovery and application of knowledge.

4. The teacher selects, uses, and maintains equipment properly, stores and disposes of chemicals safely, and handles and cares
for animals in an appropriate manner.

...