Portland Community College | Portland, Oregon

 This is a prerequisite course for MTH 212 or MTH 213.

Upon successful completion students should be able to:

• Apply an understanding of the theoretical foundations of mathematics focusing on numeration systems and operations as taught at the K-8 level in order to develop mathematical knowledge and communication skills necessary for teaching.
• Use various problem solving strategies and algebraic reasoning to create mathematical models, analyze real world scenarios, judge if the results are reasonable, and then interpret and clearly communicate the results.
• Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.
• Foster the mathematical practices in the Common Core State Standards.

In-class time is devoted primarily to small group problem solving activities and class discussion emphasizing the use of manipulatives and appropriate technology. The student’s role is to actively engage in positive collaboration with peers. The instructor's role is to facilitate and model teaching and learning practices described in the Common Core Standards.  

1. Successful completion of a non-calculator math diagnostic assessment covering pre-requisite material for the MTH 211, 212, and 213 sequence is required.  The student must pass this assessment with a minimum of 90% to receive a passing grade for the course. Multiple opportunities and interventions will be offered.
2. At least two proctored examinations, one of which must be a cumulative final.
3. At least one writing assignment
4. At least 3 hours of field experience with written reflection
5. At least two of the following additional measures:

                 a.  Take-home examinations.

                 b.  Graded homework.

                 c.  Quizzes.

                 d.  Individual/Group projects.

                 e.  In-class activities.

                 f.  Portfolios.

 1.0     MATHEMATICS AND PROBLEM SOLVING

The instructional goal is to develop problem solving ability.

1.1         Utilize and develop effective problem solving strategies with an emphasis on quantitative reasoning.

1.2         Identify deductive and inductive reasoning when problem solving.

1.3         Explore patterns and sequences, and their relationship to problem solving.

1.4         Use algebra and algebra manipulatives to problem solve.

1.5          Solve application problems utilizing functions and graphs.

2.0     SETS

The instructional goal is to learn the fundamental concepts of set theory.

2.1         Explore attributes and classification.

2.2         Represent set concepts using Venn diagrams.

2.3         Understand and use the concepts and symbols of subset, intersection, union, and complement of a set.

2.5         Utilize set theory in application problems.

3.0     NUMERATION SYSTEMS

The instructional goal is to develop an understanding of numeration systems. 

3.1         Explore numeration systems of other cultures.

3.2         Define the set of whole numbers and their properties.

3.3         Model, compute, and investigate whole number operations in several bases.

3.4         Understand place value and base 10.

3.5         Estimate and use mental arithmetic.

4.0     NUMBER THEORY

The instructional goal is to understand elementary concepts of number theory and how these concepts are used in the elementary curriculum.

4.1         Explore divisibility.

4.2         Explore the properties of prime and composite numbers, and prime factorization.

4.3        Use symbolic and visual models to investigate least common multiple and greatest common divisor/factor

4.4         Use clock arithmetic and other simple modular arithmetic applications.

Standards of Mathematical Practice

While learning the mathematical content contained in the course, the following practices will be embedded throughout and students will be assessed on their ability to:

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
9. Foster a growth mindset.