# Middle School Mathematics Endorsement

Illinois Institute of Technology's Department of Mathematics and Science Education has developed an endorsement program for elementary school and middle school teachers who want to teach middle grades mathematics in the State of Illinois. Math endorsement can be achieved by completing 15 credit hours in mathematics, 3 credit hours in methods of teaching middle school mathematics, and 6 credit hours in adolescent psychology and middle school curriculum. The 24 hour program results in an endorsement in middle grades mathematics, it does not provide an academic degree.*

**Course of Study**

- Problem-Based Algebra (3 credits)
- Problem-Based Number Theory (3 credits)
- Problem-Based Probability and Statistics (3 credits)
- Problem-Based Geometry (3 credits)
- Problem-Based Foundations of Calculus (3 credits)
- Instructional Strategies for Middle School Mathematics (3 credits)
- Middle Level and Secondary Mathematics Curriculum (3 credits)
- Adolescent Psychology (3 credits)

**Total Credits for Endorsement in Middle Grades Mathematics: 24**

**Teachers are encouraged to take the whole sequence of courses, but are allowed to take individual courses that fit their needs.**

**Suggested courses are consistent with ISBE requirements.**

**COURSE DESCRIPTION**

**MSED 509 - Instructional Strategies for Middle School Mathematics (3 credit hours)**

Instructional Strategies for Middle School Mathematics specifically addresses concerns of teaching grades 5-8 mathematics by considering the social and psychological characteristics of students in transition from elementary to high school mathematics. The course uses a focus on rational number and proportional reasoning (topics that span the middle school curriculum) to study students' development of powerful representational systems and conceptual flexibility. Participants will learn about building mathematical community in which students construct mathematical evidence for claims of perceived regularities and patterns on logical reasoning and mathematical thinking. Participants will select, adapt and design worthwhile mathematical tasks to serve various instructional purposes. Finally, the participants will learn what it means to build an on-going assessment system that integrates self-, peer-, teacher-, formative and summative assessment into a system of best practice that blurs the line between learning and assessment.

**MSED 510 - Problem-Based Algebra (3 credit hours)**

Algebra is taught via a problem solving approach with connections to other topic areas such as geometry, statistics and probability. Explorations with and conjecturing about number relationships and functions provide experiences from which students develop algebraic habits of mind: Doing and undoing (algebraic thinking that involves reflective or reverse algebraic reasoning, doing problems/procedures backwards); building rules to represent functions (recognizing patterns and organizing data to representation situations in which input is related to output by well-defined functional rules); and abstracting from computation (developing the capacity to think about computations independently of particular numbers used).

**MSED 511 - Problem-Based Number Theory (3 credit hours)**

Number theory is taught via a problem solving approach with connections to geometry, logic, and probability. Explorations with and conjecturing about number patterns provide experiences from which students study various topics including: factors, primes, and prime factorization; counting techniques; greatest common factor (GCF) and least common multiple (LCM); divisibility; number patterns (e.g., Pascal's triangle, polygonal numbers, Pythagorean triples; Fibonacci numbers); Diophantine equations; remainder classes and modular arithmetic; iteration, recursion, and mathematical induction.

**MSED 512 - Problem-Based Statistics and Probability (3 credit hours)**

This course emphasizes statistics and probability as practical subjects devoted to obtaining and processing data with a view toward making statements that often extend beyond the data. These statements (i.e., inferences) take the form of estimates, confidence intervals, significance tests, etc. The content of this course is concerned with the production of good data, and involves consideration of experimental designs and sample surveys. The activities have their origin in real data and are concerned with processing the data in the widest contexts and with a wide variety of applications such as social, administrative, medical, the physical sciences and the biological sciences.

**MSED 514 - Problem-Based Geometry (3 credit hours)**

Geometry is taught via problem solving with connections to other topic areas such as algebra and number theory. Participants use Geometer's Sketchpad to investigate about fundamental concepts of Euclidean geometry in two and three dimensions and their applications. Explorations of and conjecturing about these concepts provide experiences from which students study various topics including: properties and relationships of geometric objects; geometric proof; area and volume; transformations, symmetry and tessellations; trigonometric ratios; and visual modeling of algebraic operations and abstract algebraic concepts.

**MSED 515 - Problem-Based Foundations of Calculus (3 credit hours)**

The course is focused on the development of foundational ideas, concepts, and methods of introductory calculus and its basic applications with emphasis on various problem-solving strategies, visualization, mathematical modeling, and connections to algebra, geometry, number theory, and logic relevant to the middle school mathematics curriculum. Explorations with the SimCalc software and conjecturing about linking graphs, tables, and concrete to represent dynamic situations provide experiences from which students study various topics including: linear, quadratic, cubic, exponential, logarithmic, and trigonometric functions and their graphs; limits and continuity; rate of change, slope, tangent, and derivative; area under a curve and integration; elements of infinite series.

**MSED 555 - Middle Level and Secondary Mathematics Curriculum (3 credit hours****)**

This course is a lecture/discussion course focusing on the history/sociology of education, rationales and goals of current reform efforts, curriculum design, development, and curriculum analysis. This course helps students develop a functional understanding of the various factors that influence the development and direction of secondary science curricula, and the ability to apply knowledge of subject matter, curriculum development, and curriculum theory to construct a hypothetical curriculum that recognizes cultural and individual differences with special emphasis on the interdependence of science, technology, and society. Particular emphasis is placed on the analysis and revision of existing curriculum relative to national and state reforms.

**MSED 580 - Adolescent Psychology (3 credit hours)**

This course is designed to develop the participants' understanding of adolescent psychology. The main foci throughout the course are the unique aspects of adolescents and how those aspects influence behavior, learning, and social interactions, especially with regard to middle schools. Studies will include educational psychology theories and models, motivation and learning, developmental changes during adolescence, cognitive abilities, human ecology, diversity, and cultures. Additionally, participants will examine historical and philosophical perspectives of adolescent psychology and synthesize how these perspectives have influenced teaching, learning, and cultures in middle schools. The course will involve weekly readings and reflections, classroom experiences, short assignments, tests/quizzes, research projects, and formal class presentations.

**SAMPLE COURSE SEQUENCE**

FALL | SPRING | SUMMER | FALL | SPRING |

MSED 555: | MSED 580: | MSED 509: | ||

MSED 510: | MSED 514: | MSED 513: | MSED 511: | MSED 515: |