# Foundations of Elementary Mathematics II

## Course Description

Continues to prepare prospective elementary teachers to teach math by strengthening their mathematical background. Explores the following topics: operations involving fractions, decimals, ratio, proportion, percent, integers, also an introduction to statistics and probability. Second term of a three-term sequence. Prerequisites: MTH 211. Audit available.

## Intended Outcomes

Upon successful completion of this course, students will be able to:

1. Extend mathematical content knowledge, including:operations involving fractions, decimals, ratio, proportion, percent, integers, and introductory statistics and probability.
2. Apply various problem-solving strategies to create mathematical models that will help analyze real world scenarios which focus on fractions, decimals, percent, and statistics.
3. Use the appropriate mathematical vocabulary necessary in the teaching of elementary math.
4. Provide examples of mathematical problems which use fractions, decimals, percent, and statistics that strengthen the ability to reason, reflect, observe and engage more deeply in mathematical thinking.

## Alignment with Institutional Core Learning Outcomes

 Major 1. Communicate effectively using appropriate reading, writing, listening, and speaking skills. (Communication) Major 2. Creatively solve problems by using relevant methods of research, personal reflection, reasoning, and evaluation of information. (Critical thinking and Problem-Solving) Major 3. Extract, interpret, evaluate, communicate, and apply quantitative information and methods to solve problems, evaluate claims, and support decisions in their academic, professional and private lives. (Quantitative Literacy) Not addressed 4. Use an understanding of cultural differences to constructively address issues that arise in the workplace and community. (Cultural Awareness) Not addressed 5. Recognize the consequences of human activity upon our social and natural world. (Community and Environmental Responsibility)

To establish an intentional learning environment, Core Learning Outcomes (CLOs) require a clear definition of instructional strategies, evidence of recurrent instruction, and employment of several assessment modes.

#### Major Designation

1. The outcome is addressed recurrently in the curriculum, regularly enough to establish a thorough understanding.
2. Students can demonstrate and are assessed on a thorough understanding of the outcome.
• The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

#### Minor Designation

1. The outcome is addressed adequately in the curriculum, establishing fundamental understanding.
2. Students can demonstrate and are assessed on a fundamental understanding of the outcome.
• The course includes at least one assignment that can be assessed by applying the appropriate CLO rubric.

## Outcome Assessment Strategies

• Reflective writing
• Quizzes
• Class Discussions
• Homework
• Problem solving assignments
• Projects
• Presentations
• Exams

## Texts and Materials

Mathematics for Elementary teachers – A conceptual Approach by Bennett, Burton, Nelson, and Ediger

## Course Activities and Design

The determination of teaching strategies used in the delivery of outcomes is generally left to the discretion of the instructor. Here are some strategies that you might consider when designing your course: lecture, small group/forum discussion, flipped classroom, dyads, oral presentation, role play, simulation scenarios, group projects, service learning projects, hands-on lab, peer review/workshops, cooperative learning (jigsaw, fishbowl), inquiry based instruction, differentiated instruction (learning centers), graphic organizers, etc.

## Course Content (Themes, Concepts, Issues and Skills)

##### Outcome #1: Improve and deepen Extend mathematical content knowledge, including: operations involving fractions, decimals, ratio, proportion, percent, integers, and introductory statistics and probability.
1. Expand knowledge of Fractions
• 1.1 Operations with fractions
• 1.2 Problem solving with fractions
2. Decimals
• 2.1 Introduction to decimals
• 2.2 Operations with decimals
• 2.3 Problem solving with decimals
3. Ratios, and percent
• 3.1 Introduction to the differences of ratios and percent
• 3.2 Problem solve with ratios and percent
4. Scientific Notation
• 4.1 Applying scientific notation to real life situations
5. Real Numbers
• 5.1 Introduction to the real numbers
• 5.2 Problem solving with real numbers
6. Fundamentals of Statistics
• 6.1Collecting and graphing data
• 6.2 Describing and analyzing data
• 6.3 Using statistical models in the appropriate scenarios
• 6.4 Predicting outcomes based on statistical data
7. Probability
• 7.1 Introduction to the fundamentals of probability
• 7.2 Interpreting results from various types of events
##### Outcome #2: Apply various problem-solving strategies to create mathematical models that will help analyze real world scenarios which focus on fractions, decimals, percent, and statistics.
• Demonstrate the problem-solving strategies which include: drawing, guessing and checking, making a table, working backwards, finding a pattern using fraction bars
• Use technology to verify and compare the outcomes of various mathematical models in statistics and probability.
##### Outcome #3: Use the appropriate mathematical vocabulary necessary in the teaching of elementary math.
• Show how mathematical vocabulary is necessary to explain problems
• Compare and contrast non-mathematical vocabulary with proper mathematical vocabulary.
##### Outcome #4: Provide examples of mathematical problems which use fractions, decimals, percent, and statistics that strengthen the ability to reason, reflect, observe and engage more deeply in mathematical thinking.
• Demonstrate the steps (algorithms) needed for fractions, decimals, ratios, percent, fundamental statistics and probability and explain how they work.
• Explain the thought processes used when analyzing various types of data used in statistics/probability such as graphs, charts, and other data in various formats.
• Use technology to model the similarities and differences between fractions, decimals, percent, and probability.
• Identify how application problems using fractions, decimals, percent, and statistics can be modeled mathematically.