MODULE 1
Module Title
: Fundamental Concepts
Estimated time to complete:
Five 75 minute periods
Module objectives:
The student will be able to:
- Access and evaluate an elementary level interactive web site.
- Demonstrate competencies in understanding Venn Diagrams, operations with sets, manipulations in algebraic expressions representing real world problems, and understanding various numeration systems, bases, and place value.
- Distinguish the advantages and disadvantages of each method of delivery: text, hands-on manipulatives, and interactive educational sites.
Concept(s) learned in this module:
Accessing and evaluating interactive web sites
Communicating student understanding of different pedagogical styles via journal writing
Demonstrating competencies in sets, algebraic thinking, and the foundations of numerations
Standards addressed in this module:
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
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
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-enhanced instructional strategies utilized in this module:
Technology-enriched problem-based learning
Computer-based simulations/games/role-playing
Web-based learning
Electronic portfolio development
Technology-enhanced demonstrations
|
Components |
Brief description of module activities |
Student
Grouping |
Materials/
Technology |
|
Engagement |
KWL Chart or Concept Map of personal information regarding sets, algebraic thinking, and numeration
|
Individual or whole class |
Word processing |
|
Exploration |
Prior to class instruction, students visit a given interactive web site(s) and play a game or complete a task that requires using the specific content objectives. Students complete admit slip reflections on their work at the assigned site. |
Individual or in pairs |
Computer with internet access |
|
Explanation |
Teacher facilitates classroom instruction on objectives incorporating text materials, hands-on manipulatives, and interactive sites as applicable. Students complete learning log questions. |
Whole class |
Computer with internet access |
|
Extension
|
Students explore additional web sites pertaining to the topic at hand.
|
Groups of four |
Computer with internet access |
|
Evaluation |
Student completes a module summary reflecting one of the content areas covered. Summary to include comparisons of text, hands-on manipulatives and interactive educational sites to enhance learning. |
Individual |
Electronic journal entries |
Expected module outcomes
:
The student will be able to:
- Access and evaluate an elementary level interactive web site.
- Demonstrate competencies in understanding Venn Diagrams, operations with sets, manipulations in algebraic expressions representing real world problems, and understanding various numeration systems, bases, and place value.
- Distinguish the advantages and disadvantages of each method of delivery: text, hands-on manipulatives, and interactive educational sites.
Performance-based assessment of module outcomes:
Students will complete a module summary in an electronic journal based on comparisons of text, hands-on manipulatives, and interactive educational sites. This module summary will be used in the culminating unit activity (see Unit Overview).
Module Summary Rubric:
|
Excellent |
Adequate / Good |
Fair |
Poor |
|
Each bullet is
5 points |
Each bullet is
4 points |
Each bullet is
3 points |
Each bullet is
2 points |
- Excellent description of the web activity
- Clearly states content objective(s) including NCTM Standards addressed
- Compares / contrasts site vs. text vs. manipulative (as applicable) including advantages / disadvantages of each
- Each question has a substantive response
- Posted by deadline
|
Adequate description of the web activity
Clearly states content objective(s)
- Adequate compare / contrast site vs. text vs. manipulative (as applicable)
- Each question has an adequate response
- Posted by deadline
|
Fair description of the web activity
States content objective(s)
- At least two questions have adequate responses
- Posted by deadline
|
Poor description of the web activity
Minimally states content objective(s)
- At least one question has an adequate response
- Posted by deadline
|
|
Maximum Points: 25 |
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