
Things We Do
Student Outcomes
 Application problems
 Some symbol manipulation skills
 Verification and reasonableness of answers
 Estimation
 Good communication
 Patterning
 Multiple models
 Units
 Interpreting results
 Approximate numbers
 "One Step" Calculator Computations
Pedagogy
 Understanding of concepts
 Guided discovery activities
 Active classroom
 Collaborative learning
 Visual learning
 Handson materials
 Integrate technology
 Integrated review
 Geometry integrated throughout
 Course outlines / textbook adoption list
Things We DON'T Do
 Complicated arithmetic without calculators
 "Exact" answers over approximations
 Contrived complicated algebraic manipulation
 Chapter tests
 Cover one section per day
 Algebraic manipulation with no/limited application at this level. e.g. factoring trinomials, simplifying rational expressions, complex number arithmetic, etc.
 Teach "black box" algorithms or calculator techniques
Things We Do
Student outcomes
 Application problems
Applications are fully integrated. Whenever possible, real world data should be used.
 Some symbol manipulation skills
Algebraic manipulation has been deemphasized, but not removed. It is important the students master the skills we have chosen to cover.
 Verification and reasonableness of answers
As much as possible, students are expected to determine the correctness of their answers. Students should numerically verify all symbolic manipulations. For all application problems, it is expected that students consider the possibility of their answer actually happening in the real world.
 Estimation
Estimation is helpful for checking calculator results, and solving some application problems. Estimation is useful when exact values are not available, when using precise numbers is too difficult, inconvenient or costly and when all that is needed is an general idea of how large something is.
 Good communication
Students are expected to communicate their ideas, processes and understanding orally and in writing.
 Patterning
Mathematics is the study of patterns. We use patterns help students to make mathematical rules  for example, we multiply negative numbers together and notice that we always seem to get a positive number. We encourage students to explore situations numerically and then look for patterns to find algebraic representations.
 Multiple models
Students are introduced to algebra with verbal descriptions, numerical models, graphical models, and algebraic models. They should be able to choose the appropriate model for a given situation and should be able to use one of the models to create the others, if possible. Connections between the models is stressed.
 Units
Unit analysis is incorporated throughout the curriculum. Emphasis is placed on the correct use of units in all situations. Students should know what units mean in a situation  for example, they should recognize that it would not make sense to say that a the area of a lot is 24 meters.
 Interpreting results
Whether information is presented graphically, numerically, or algebraically, it is only useful if it can be interpreted in a particular situation. Therefore, students are continually asked to interpret information represented mathematically. A good question to ask is "So what does your answer tell you about the situation?"
 Approximate numbers
All measurements are approximate, as the measurement can only be as accurate as the tool used. Students should use appropriate rounding in application problems.
 "One Step" Calculator Computations
In general, it is preferable to enter long numerical expressions into the calculator in one step. (i.e. only hitting enter once.) This makes repeated calculations easier, and helps students start the patterning process need to create algebraic expressions in applications.
Things We Do
Pedagogy
 Understanding of concepts
It is not enough for students to mimic processes. They are expected to know why things work the way they do.
 Guided discovery activities
Students are more likely to understand concepts if they have had a chance to work with them in activities designed to draw their attention to rules, patterns, etc. The activities cannot stand alone  they must be followed up with clear explanation. Guided discovery is not the same as just letting the students figure out for themselves.
 Active classroom
 Collaborative learning
Students benefit from communicating mathematics, sharing different approaches, being more actively involved, and they attain a deeper understanding by explaining concepts to others. Teamwork creates a more positive learning environment in class.
 Visual learning
Visual learning is incorporated throughout the curriculum to address the needs of visual learners.
 Handson materials
Handson materials are used to make abstract mathematics more concrete. A large variety of maniuplatives are available.
 Integrate technology
Calculators and graphing calculators have impacted what we teach and, more exciting, how we teach.
 Integrated review
Once a concept is introduced, related problems are sprinkled throughout the course.
 Geometry integrated throughout
Geometry is used throughout all the classes. We don't have a separate geometry course.
 Course outlines / textbook adoption list
Teach what is in the course outline or textbook adoption list. If you leave something out, the students won't be prepared for the next class. If a topic isn't in there, it is either in a different course, or has been taken out for a reason. There is so much material in each course that any additions would displace other material.
Things We DON'T DO
 Complicated arithmetic without calculators
Students can be expected to be able to do SIMPLE (single digit numbers) arithmetic without calculators, but that is all. They should be able to estimate answers  they don't have to be able to multiply 64*872, but they should be able to estimate it using 60 * 900 or possibly 50 * 1000.
 "Exact" answers over approximations
In general, numerical approximations are more useful in applications than messy exact answers (with radicals, complicated fractions, etc).
 Contrived complicated algebraic manipulation
 Chapter tests
 Covering one section per day
 Algebraic manipulation with no or limited application at this level. e.g. factoring trinomials, simplifying rational expressions, complex number arithmetic, etc.
Students are not expected to learn certain skills, just because they have always been taught.
 Teach "black box" algorithms or calculator techniques
Students should not be taught algorithms until they are able to understand why they work. The same is true for calculator techniques. For example, graphing is not taught until students know how to create graphs by hand  the calculator is just used because it is faster and more accurate.

