Course Description

To be a mathematician is to be a logical problem solver.

You will have problems. Some will be mathematical. You will need to do your budget, file taxes, scale a recipe, etc. All of this is basic algebra. However, the truly meaningful problems in life require a brain that is disciplined and logical. More than anything what we’ll be doing in here is developing those habits of mathematical thinking and interaction, or as I will often call it, your mathematical brain.

It is my belief that all students can learn to think logically through math. It is my belief that these habits of interaction help students build critical thinking and reasoning that are useful in a far greater capacity that math itself.

The academic goal of this course is to prepare students for post-secondary level mathematics courses like Math 95 and 105 as offered a Clackamas Community College. We will be making sense of the math by justifying why things work and generalizing math operations with conjectures.

To do this we must:

• Reason about mathematical regularity, patterns, and structures that are repeatable.
• Create and reason from mathematical representations - visual models, graphs, equations, situations, symbols, etc.
• Notice and reason about connections within and across mathematical representations
• Explore mistakes and stuck points to start new lines of reasoning and learning
• Use metacognition and reflection to think about thinking
• Persevere and seek more! Welcome challenging problems and explore new problems!

This work is challenging and we cannot do it alone. We will need to work together to collaborative discover the truth about mathematics to make sense of it. We will interact with each other by practicing the following habits:

• Use private reasoning time to develop our own understanding of problems;
• Explain to others what we know and understand;
• Listen to understand what other think and learn from them;
• Ask genuine questions about the problems we see to each other;
• Explore multiple pathways as there are multiple ways to solve problems;
• Compare our logic and ideas to better see how others think;
• Critique and debate our ideas to find the best possible method;
• Recognize that math reasoning is the authority, not the teacher, test, grade, or points.

Logic and math exist, awaiting to be discovered. We can only see it when we train our brains to recognize these beautiful patterns and relationships that exist whether or not we see them. I greatly look forward in guiding you on this journey towards unlocking your logical, mathematical brain.

Course Objectives

Pre-College Contemporary Mathematics (PCCM) is a two term course for 1 math credit. I have designed it to build on Algebra 1 and Geometry principles to prepare students for the concepts taught in Math 95 and 105.

Material is pieced together from the Math Vision Project, a Common Core aligned curriculum available for free online at mathematicsvisionproject.org. We will use parts of the Secondary Mathematics Three course with some supplemental material drawn from Secondary Mathematics Two and Illustrative Mathematics.

In section A we will cover the following topics:

• Module 1: Functions & Their Inverses
• Module 2: Logarithmic Functions
• Module 3: Polynomial Functions
• Module 4: Rational Expressions and Functions

Along with Illustrative Math topics on topics such as: “Exponential Parameters”,  “Rising Gas Prices – Compounding and Inflation”, “A Saturating Exponential”, “Pizza Place Promotion”, “Powers of 11”, “Uranium 238”, “Profit of a Company”.