The Brehm Department of Mathematics is focused on meeting the diverse needs of students with learning disabilities. The core concern of Brehm’s mission revolves around empowerment. For many of our students, mathematics has been a source of anxiety, frustration, and, often, failure. Therefore, for students to develop an internal locus of control and to be empowered in this curriculum area, we must always begin with creating the sense that mathematics is both a worthwhile endeavor and success is an attainable goal. On the other end of the spectrum, we also have many students who are very capable or even excellent math students who may need to be supported in other disability areas such as reading, writing, or executive functioning.

Consequently, the math department designs, modifies, and implements curriculum so that students can be best served given their individual math strengths and weaknesses. To accomplish this, we must understand the students’ overall skill levels, where they have their peaks, valleys, or holes, and how other areas may impact their math work (such as reading, writing, executive functioning or self-management.) The whole child must always take center stage as we progress through the curriculum to develop their potential at the remedial level, algebra I, pre-calculus, or beyond. Care is taken to teach for mastery and skill development while at the same time extending their boundaries to the higher ends of upper-level math and its rigor. A balance must be struck as they progress forward while not repeating a similar pattern of anxiety, frustration or failure.

The math curriculum is designed to meet the educational goals set by the State of Illinois, which are also aligned with the goals set forth by the National Council of Teachers of Mathematics. The core goals encompass the following:

- Numbers
- Calculations
- Measurement
- Estimation
- Algebra
- Geometry
- Trigonometry and other advanced math topics
- Statistics, data manipulation, and probability

Additionally, opportunities are provided for basic skill development or maintenance, graphing, measurement, and preparation and practice for standardized tests. These core goals are also expressed through applications, problem-solving, written and verbal communication, the use of technology, cooperative groups, and connections to other disciplines. Technology has always had an essential role at Brehm. We have long used personal computers to explore mathematical relations and as an assistant in communication. Currently, each student and staff member has a personal laptop computer that is equipped with standard and scientific calculators as well as Geometers Sketchpad, Grapher, and Numbers, all of which have direct mathematical applications. Additionally, Pages and Keynote provide a variety of ways to manipulate and explore content and to communicate more effectively.

Given our small class size and aggressive technological footprint, individualization is a leitmotif throughout our classes. Students are exposed to whole-class instruction and whole-class objectives while given opportunities to remediate deficit areas or supplemental work to extend upon the core of learning or to work at a higher Bloom’s level. In some cases, a “class within a class” may develop where a group of students works at different levels or paces. Our emphasis on the needs of the individual student allows the student to work comfortably through Illinois and national standards as well as the Brehm competencies at a pace and manner suiting their needs. We use frequent short homework sets, quizzes, tests, pre/post-testing, curriculum-based assessments, and observations to assess this diversity. With this information, we can reflect upon the student’s performance on the topics presented, and form (or reform) instructional arcs to move ahead in the curriculum and solidify previously learned skills.

The scope of our courses is consistent with a standard high school curriculum. However, the material is modified regarding reading levels, number of problems, breadth of topics, and the pace of the presentation. Aside from the remedial classes, it is generally accepted that our students can learn the standard material but not necessarily in the standard time frames or the standard manner. Therefore, the textbooks we use often undergo modification through reduction, paring down, supplementation, and elaboration. Our classes draw from textbook publishers such as AGS and Key Curriculum Press to other standard publishers.

As previously mentioned, our instructional methods cover a range of strategies and modalities that vary with the specific content, students, or classroom makeup. The small class sizes make it easy to move from whole-class teacher-centered instruction to cooperative groups and individualized instruction. New concepts are often presented to the whole or cooperatively, with follow-up presented individually. All classes are equipped with a projection unit tied into the teacher’s laptop, which allows for whole-class presentation, while other courses have document scanners and overhead projectors. Students can access primary class documents (handouts, copies of notes, scans of textbooks) as well as examples, videos, photos, and other supplemental material via the Public Documents folder on their laptops. Students also have ready access to calculators, graphing software, as well as the iWorks suite of software, which allows them to record or film lectures with Garage Band or iMovie, to take photos of the whiteboard with Photo Booth, etc. Additional classroom strategies include pre-teaching vocabulary and showing worked examples, providing mnemonics, and utilizing varying modalities such as sight, touch, and sound. Hands-on activities involve the use of manipulatives such as fraction blocks and Cuisenaire rods for general math or algebra. Executive functioning approaches are used, including advanced organizers, flow charts or outlines, chunking, task analysis, etc. The students work through instruction from concrete, to the semi-concrete, to the semi-abstract, to the abstract level of learning. Visualizing and Verbalizing is used to help the students work through word problems.

Collaboration between the instructors in the math department generally focuses on reviewing and discussing individual student strengths, weaknesses, and strategies that have worked for that student in the past or have been successful with similar students. The math faculty have attended local, regional, and national workshops. Sharing and refining material between instructors is also very common since we tend to teach various courses from one year to the next.

##### Offered Courses:

##### Junior High Math:

This class is designed for junior high school students requiring more of a remedial approach. It is a survey of broad foundation concepts in math and the application of those concepts to projects designed to mimic real life situations. There is a heavy emphasis on the basics of arithmetic and geometry.

##### Pre-Algebra:

This course is intended for the student who has successfully completed the concepts developed in basic math instruction. Instruction includes:

- Ratios and proportions
- Operations with integers, exponents, and square roots
- Introduction to geometric concepts
- Introduction to coordinate graphing
- Fractions, decimals, and percents
- Solving basic linear equations

##### Algebra I/Algebra I Extended:

This course is intended for students who have successfully mastered and completed the concepts as outlined in the Pre-Algebra course. Instruction includes:

- Review of the rules of arithmetic and number sense (where needed)
- Operations with integers
- Order of operations
- Linear equations
- Applications (word problems)
- Laws of exponents
- Systems of equations
- Polynomials operations
- Quadratic equations
- Coordinate graphing
- Data Analysis and Probability

##### Algebra II/Algebra II-Extended:

This course is intended for students who have completed Algebra I/Algebra I Extended or have demonstrated basic competency in algebra. This course is designed for students who possess strengths in mathematics and are inclined to pursue a college career. Topics include but are not limited to:

- Linear functions, linear equations, and inequalities,
- Functions including absolute value, square root
- Factoring of polynomials
- Solving quadratics and quadratic graphing,
- Operations on polynomials, rational expressions, powers, roots, radicals, exponents, and complex numbers
- Logarithm and exponential equations
- Pythagorean theorem
- Trigonometry.
- Circle trigonometry
- Non-right triangle trigonometry

Complex numbers

##### Geometry:

This course is designed to provide both experiential and abstract knowledge of the geometric world for both the college and non-college bound student. Students will be exploring geometric concepts and spatial relations using available geometric software. Topics include but are not limited to:

- Properties and relationships of parallelism, quadrilaterals, triangles, and other polygons
- Properties and relationships of circles
- Properties and relationships of 3-dimensional structures
- Pythagorean Theorem
- Trigonometric relationships

Skills and processes development include:

- Sketching geometric figures
- Angle and length measurements and scaled drawings
- Perimeter, area, volume, and surface area
- Graphing and coordinate geometry

##### Principles of Algebra and Geometry:

This class focuses on the key concepts of Algebra and Geometry. This class is includes the following topics:

- Review of the rules of arithmetic and number sense
- Operations with integers
- Order of operations
- Linear equations
- Continued topics in algebra such as quadratic functions and polynomials
- Applications (word problems)
- Sketching geometric figures
- Properties and relationships of: parallelism, quadrilaterals, triangles, and other polygons
- Length measurements and scaled drawing
- Perimeter, area, volume, and surface area