UNIT TITLE: Integrating Website Activities in Math for Elementary Teachers

Unit Goal: To integrate web-based activities with text and hands-on manipulatives in the teaching of mathematics content to pre-service teachers

Unit Summary: The four modules contained in this unit represent templates for the inclusion of content based, interactive websites throughout a semester long mathematics course for pre-service teachers. The modules’ sequence is based on Chapters 2-5 of Mathematics for Elementary School Teachers(Houghton Mifflin, 2nd Ed) by Tom Bassarear. This text is supplemented by the text author’s Mathematics for Elementary School Teachers: Explorations and a Start with Manipulatives Kit from ETA/ Cuisenaire. In each module, students are asked to explore and reflect on a given content based website prior to classroom instruction. (A recommended site is given for each module) Following content instruction (which include additional web-based activities and hands-on manipulatives, investigations and lecture) students are required, in teams, to research other web sites which provide additional opportunities for content enhancement. Their findings are then reported back to the class at the close of the semester.

Grade Level (K-16): 13-15

General Subject Area(s): Math for Elementary School Teachers

Minimum time required for the unit: 1 Semester

Concepts learned across all unit modules:

• Accessing and evaluating interactive web sites
• Communicating student understanding of different pedagogical styles via journal writing
• Demonstrating competencies in addition, subtraction, multiplication, and division with respect to the given numeration system
• Recognizing patterns and properties of the fundamental operations
• Demonstrating competencies in whole, integer, rational and real number operations

Standards addressed by unit modules:

Praxis:

Mathematics Curriculum, Instruction, and Assessment

Teaching strategies and activities that will aid in the development, delivery, and evaluation of the following:

• Curriculum components – for example, scope and sequence of skills and materials; appropriate materials and technology; learner objectives
• Use of manipulatives and developmentally appropriate materials; variety and reliability
• Pre-number and number concepts – for example, counting objects, comparing objects; classifying objects; exploring sets; ordering sets; number patterns
• Problem solving – for example, investigate and understand content; formulate problems from everyday situations; develop strategies applicable to a wide range of problems; verify and interpret results; build student confidence; identify and solve problems that are developmentally appropriate
• Content specific pedagogy – for example, theories necessary for implementing a sound instructional program such as accessing prior knowledge, constructing knowledge, modeling, informal reasoning, graphic organizers
• Addition and subtraction of whole numbers – for example, computational procedures; relationships between addition and subtraction; relationship between subtraction and division; regrouping; modeling the operations; story problems
• Multiplication and division – for example, modeling the operations, interpretations for the operations; computational procedures; skill development; story problems
• Concepts related to number theory – for example, factors, multiples, primes and composites, remainders, odd and even
• Rational numbers – for example, fraction and decimal equivalence; computation; modeling

Conceptual Knowledge and Procedural Knowledge

Demonstrate number sense and operation sense, that is, an understanding of the foundational ideas of numbers, number properties, and operations defined on numbers.

• Order: demonstrate an understanding of order among whole numbers, fractions, and decimals
• Equivalence: demonstrate an understanding that a number can be represented in more than one way
• Numeration and place value: demonstrate an understanding of how numbers are named, place value, and order of magnitude of numbers
• Number properties: demonstrate an understanding of the properties of whole numbers without necessarily knowing the names of the properties
• Computation: perform computations; adjust the result of a computation to fit the context of a problem; identify numbers or information or operations needed to solve a problem
• Equations: solve simple equations and inequalities; predict the outcome of changing some number or condition in a problem
• Estimation: estimate the result of a calculation; determine the reasonableness of an estimate
• Algorithmic thinking: demonstrate an understanding of the algorithmic point of view — that is, follow a given procedure; recognize various ways to solve a problem; identify, complete, or analyze a procedure; discover patterns in a procedure

Formal Mathematical Reasoning

Demonstrate an ability to use the basics of logic in a quantitative context.

• Logical connectives and quantifiers: interpret statements that use logical connectives (and, or, if – then) as well as quantifiers (some, all, none)
• Validity of arguments: use deductive reasoning to determine whether an argument (a series of statements leading to a conclusion) is valid or invalid
• Generalization: identify an appropriate generalization, an example that disproves an inappropriate generalization, or a hidden assumption

NETS:

Demonstrate the ability to:

• Use technology tools and information resources to increase productivity, promote creativity, and facilitate academic learning.
• Use content-specific tools (e.g., software, simulation, environmental robes, graphing calculators, exploratory environments, Web tools) to support learning and research.
• Use technology resources to facilitate higher order and complex thinking skills, including problem solving, critical thinking, informed decision making, knowledge construction, and creativity.
• Use technology to locate, evaluate, and collect information from a variety of sources.
• Observe and experience the use of technology in their major field of study.

Technology needed in unit modules:

• Computer with internet access
• Computer with Power Point software
• Projection device for computer

Technology-enhanced instructional strategies employed:

• Technology-enriched problem-based learning
• Computer-based simulations/games/role-playing
• Web-based learning
• Electronic portfolio development
• Technology-enhanced demonstrations

Title of Each Module:

#3 – Number Theory

Unit Culminating Activity: Student groups (four person) will present their website research results for the four chapters. These presentations will include: demonstrations of the web sites, evaluation of the websites, a comparison of website activity to text’s and hands-on manipulatives’ approaches (as applicable) to the content area, and a written commentary. The commentary is to include: a summary of the individual chapter reflections, a personal reflection of their individual process in the acquisition of their chosen websites, a comparison of website activity to text’s and hands-on manipulatives’ approaches (as applicable) to the content area and a description of the content skill(s) could be enhanced by a student using the web-based activities.

View the Culminating Activity Rubric

Unit Authors: John August

Chris Jarvis

Nancy Lewis

Sophia Ritz