Geometry
Cohort
Instructor: David CusterClass Time: 4:00 – 8:00
unless otherwise noted / Location: Salem High School
Room 231
Note: Changes and adjustments may be made to this syllabus when judged appropriate by the instructor. Such changes, should they occur, will be announced in class or emailed.
The mission of Metro RESA is to provide research-based, high quality, systemic, results-driven, job embedded, and standards-based professional learning opportunities for the P-12 educators of the Metro Atlanta area in order to support the highest level of student learning for every P-12 child.
Purpose: PSC Standards –2 ii, iv, v, vii, viii, 3, 4, 5, 6, 7, 8 v, viii, 9, 10, 11, 12, and 13
This course focuses on preparing P-5 mathematics specialist candidates to:
· Broaden understanding of fundamental concepts of geometry with particular attention given to specific methods and materials of instruction.
· Solve measurement and geometry problems using multiple strategies, manipulatives, and technological tools.
· Construct and justify arguments as well as interpret solutions; and determine reasonableness of answers and efficiency of methods.
· Nurture collaboration, critical thinking, hands-on exploration, manipulative use, problem-based inquiry, technology utilization, and activity implementation addressing various learning styles.
· Select and use a variety of formative and summative assessment techniques to monitor student progress, gauge students’ mathematical understanding, and interpret school-based progress.
The principal geometry topics to be taught in this course are: introductory geometry, constructions, congruence, similarity, concepts of measurement, motion geometry, and tessellations.
TEXT:
Van de Walle, John. (2004). Elementary and Middle School Mathematics: Teaching Developmentally. 5th Edition. New York: Pearson.
Chapters 19 and 20
Learning Outcomes: PSC Standards – 2 ii, iv, v, vii, viii, x, xi, 5, 7, 8 iv, v, vii, and 14
Students participating in this course will learn to:
· Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;
· Specify locations and describe spatial relationships using coordinate geometry and other representational systems;
· Apply transformations and use symmetry to analyze mathematical situations;
· Use visualization, spatial reasoning, and geometric modeling to solve problems.
· Understand measurable attributes of objects and the units, systems, and processes of measurement; and
· Apply appropriate techniques, tools, and formulas to determine measurements.
· Demonstrate a deep understanding of how P-5 students learn mathematics and of the pedagogical content knowledge appropriate to P-5 mathematics teaching.
Course Objectives: PSC Standards – 2 ii, iv, v, vii, viii, x, xi, 5, 7, 8 iv, v, vii, and 14
All students will be able to demonstrate:
1) an understanding of standard vocabulary and symbols of elementary mathematics;
2) an ability identify, describe, visualize, classify and compare one, two, and three-dimensional shapes;
3) a confidence, desire, and ability to use estimation to facilitate solving geometric and measurement problems;
4) an ability to use geometry in real-world problem solving;
5) a well-developed spatial sense including both two- and three-dimensional figures (tessellations, symmetry, congruence, similarity, polygons and other curves, polyhedra);
6) an understanding of geometry and measurement from a historical perspective;
7) an ability to apply the process of measurement to one-, two-, and three-dimensional objects using nonstandard and customary geometric units.
8) an ability to solve measurement problems involving perimeter, circumference, area, volume, temperature, and mass;
9) an understanding of coordinate, and transformational geometry with an emphasis on problem solving;
10) an understanding of the uses of a variety of manipulatives, technology, and other materials for the P-5 level;
11) an understanding of the vision of mathematics education as put forth in NCTM's Principles and Standards (2000);
12) an understanding of the scope and sequence of elementary school mathematics programs;
13) a knowledge of current professional literature in the field of mathematics education.
Attendance Policy – Candidates must attend no less than 90% of the class sessions. For the 50 hour class, candidates must be in class no less than 45 hours.
Assignments
All assignments must be submitted on the due date. If you are absent on the day an assignment is due, please email your work or make arrangements to send work with a classmate. The assignments listed below are sample pieces of evidence to show the candidate has met the identified objective(s). The correlated outcomes and objectives are in parenthesis at the end of the description. The number refers to the outcome and the letter refers to the objective. The Roman numerals refer to the PSC P-5 Mathematics Program Standards.
G. 1 – Scope and Sequence
Compare and contrast the NCTM scope and sequence with the GPS scope and sequence for K-5 geometry. (7.d)
Exemplary / Acceptable / In ProgressG. 1 – Scope and Sequence / In addition to providing evidence at the acceptable level, a justification is made for the differences noted between the two NCTM and GPS scope and sequence. / The comparisons and contrasts between the NCTM scope and sequence for K-5 geometry with the GPS scope and sequence for K-5 geometry are accurate and complete. Analysis across grades K – 5 is expected. / The comparison and contrasts made are inaccurate or incomplete (does not include the entire grade band).
G. 2 – Vision of Mathematics Education
Complete a narrative of no more than 150 words describing the vision of mathematics education as it relates to geometry from NCTM’s Principles and Standards (2000). (7.c)
Exemplary / Acceptable / In ProgressG. 2 – Vision of Mathematics Education (7.c) / In addition to providing evidence at the acceptable level, a description of how the vision guides the teacher’s work is included in no more than 150 words. / Original narrative of 150 – 250 words accurately describes the vision of mathematics education as it relates to geometry from NCTM’s Principles and Standards (2000). / An incomplete or inaccurate description OR non-specific description to geometry is provided.
G.3 – Professional Literature
Compile an annotated bibliography of literature specific to the field of mathematics education as it relates to geometry. (7.e)
Exemplary / Acceptable / In ProgressG.3 – Professional Literature
(7.e) / In addition to providing evidence at the acceptable level, the candidate describes how he/she used at least 3 of the literature selections in the development of the unit. / The annotated bibliography of literature specific to the field of mathematics education as it relates to geometry includes at least 10 entries with specific descriptions (of 60 words or less). At least one of the entries is used in the unit. [FYI - There are 50 words in this cell.] / The bibliography lacks 10 entries OR the descriptions do not provide enough information about the source.
G. 4 – Transformations, Similarities, and Congruence (evaluated on test)
G. 5 – Instructional Materials
Provide a choice of and rationale for the use of one appropriate manipulative, use of technology, or other material for each of the concepts listed: coordinate geometry, transformations, tessellations, symmetry, congruence, similarity, linear measurement (customary and metric), volume, temperature, mass, perimeter, circumference, area. (7.b)
Exemplary / Acceptable / In ProgressG. 5 – Instructional Materials / In addition to providing evidence at the acceptable level, samples of student work demonstrating the use of the manipulatives or technology are provided for at least 1 of the concepts.
SUMMER - If participants do not have students during the course, a brief description of a task that will yield a student work sample is provided for at least 2 of the concepts. / A choice (1) of and rationale for the use of appropriate manipulatives and other materials is provided for each of the concepts listed: coordinate geometry, transformations, tessellations, symmetry, congruence, similarity, linear measurement (customary and metric), volume, temperature, mass, perimeter, circumference, area. Technology is included for at least 3 of the concepts. / One or more of the concepts is/are missing OR an inappropriate manipulative is described OR the rationale is not appropriate.
G. 6 - Mathematical Vocabulary
Maintain an organized list of all of the identified mathematical terms used in the course. Provide representation of the term using Venn diagrams, Frayer models, word maps, pictorial representations or others. (7.a)
Exemplary / Acceptable / In ProgressG. 6 - Mathematical Vocabulary (7.b) / In addition to providing evidence at the acceptable level, samples of work from at least 3 students are provided showing evidence that students understand at least 10 mathematical terms.
SUMMER – Candidates can do one of the following:
1) Describe a plan for vocabulary instruction in mathematics.
2) Identify and represent at least 5 other geometric terms in addition to those covered in this class. / Evidence is provided of the candidate’s understanding of all of the identified vocabulary terms using Venn diagrams, Frayer models, word maps, pictorial representations or others. / Incomplete, inappropriate, or incorrect representations are provided.
G.7 - Unit
Culminating Activity: Developing an Instructional Unit
During this course, students will develop a unit of instruction (five days of lessons excluding the pre- and post test) for the geometry strand to teach at their grade levels. The teaching unit is to serve as the culminating assessment and to address best practices for mathematics at the elementary level and PSC Standards 2 ix, x, xi, 4, 5, 6, 9, 10, 11, and 12 for the Early Childhood endorsement. The unit offers an opportunity for the teacher to connect with other instructional areas both across mathematics strands and with other disciplines.
The teaching unit must include the following:
1) Strategies addressing diversity (gender, ethnicity, learning styles, etc.) to support full participation by all students;
2) Appropriate use of technology, print and electronic resources, and manipulative and visual materials;
3) Interdisciplinary activities and problem solving;
4) Effective uses of student groupings such as peer teaching and collaborative grouping;
5) Varied instructional strategies based on current research and local, state, and national standards;
6) Formative and summative assessments to determine student achievement;
7) NCTM Standards addressed; and
8) GPS and elements addressed.
First half of the course (Part One):
9) Choose organizing topic and GPS and elements
10) Clarify GPS (a brief clarification if necessary)
11) Develop essential question for the unit
12) Develop concept map for the unit
13) Develop essential questions for the lessons
DUE DATE for Part One: (about 4 weeks into the course- or 1/3 of the length of the course)
In the second half, but prior to the end of term (Part Two):
Revise Part One
14) Design culminating activity
15) Design rubric for the culminating activity
16) Develop the launch activity (capture attention and engage learners)
17) Develop the acquisition lessons (lessons for students to acquire knowledge), at least one lesson for each essential question
18) Develop the extending/refining lessons (lessons that extend the content)
DUE DATE for Part Two: (about 7 weeks or 7/12 of the length of the course)
At the end of the term (Part Three): (about 5/6 of the length of the course)
Revise Part Two
19) List resources and materials
20) Develop timeline, pacing guide
21) Specify differentiation methods
Geometry Unit Rubric
Name______Date ______
/Exemplary(3)
/ Acceptable (2) / Not Acceptable (1) /Connection to Standards
(7, 8, 9, 10) / In addition to the Acceptable level, an explanation is provided about how the unit related to national standards. / Unit directly relates to state standards. / Less than 90% of the unit activities and assessments relate to state and national standards.
Incorporation of research based exemplary instructional practices
(4, 5, 10, 11, 12, 13, 16, 18, 21) / In addition to the Acceptable level, an explanation of the research regarding one of the instructional practices is provided. / Unit includes best practices of launch activity, vocabulary, essential questions, activating strategies, distributed practice and summarizing, graphic organizers including a concept map, and extending/refining activities. / Unit includes less than 6 exemplary instructional practices.
In addition to the Acceptable level, an explanation is provided for at least 2 different student groups. / Unit includes a variety of student grouping (independent learning, cooperative pair, peer teaching, collaborative grouping). / Unit does not use multiple student groups.
Learning Tools
(2, 19) / In addition to the Acceptable level, an alternate type of manipulative or visual aid for two learning activities are suggested. / Appropriate use of manipulatives and visual aids throughout the unit / Inappropriate or no use of manipulatives and visual aids
Culminating Project or Performance Assessment
(15) / Project or performance is an authentic application that requires complex thinking and is directly connected to the standards for the unit. / Project or performance requires complex thinking and is directly connected to the standards for the unit but may lack authenticity. / Project or performance measures student knowledge level without using complex thinking and/or the assessment is not directly linked to the standards.
NCTM Principle:
Equity
(1, 4, 21) / In addition to the Acceptable level, an explanation is provided describing how scaffolding and extensions were selected. / Unit sets high expectations for all students and includes strategies to support participation by all students. / Unit does not address high expectations and/or includes strategies to support full participation by all students.
NCTM Principle:
Curriculum
(5, 16, 17, 20) / In addition to the Acceptable level, an explanation is provided about the importance of the concept. / Unit is coherent and focused on important mathematics. A timeline and pacing guide are included. / Unit is a collection of activities that are not focused on the standards.
NCTM Principle:
Learning
(5, 17) / In addition to the Acceptable level, an explanation is provided about how the unit builds on prior knowledge from previous grades. / Unit provides a plan for developing conceptual and procedural understanding for students by actively building new knowledge from experience and prior knowledge. / Unit provides a plan for developing either conceptual or procedural understanding but not both.
NCTM Principle:
Assessment
(6, 14, 15) / In addition to the Acceptable level, the summative assessment indicates what standards are addressed by the different tasks or items. / Unit has both formative and summative assessment of all learning (with specific feedback if the unit was taught). The rubric describes at least 3 performance levels for at least 3 criteria (at least 9 cells). / Unit has only summative assessment and little feedback.
NCTM Principle:
Technology
(2) / Unit incorporates the use of student focused technology for enhancing student learning. / Unit incorporates the use of technology but may be teacher focused rather than student focused. / Unit does not incorporate technology or technology recommended will not increase student learning.
NCTM Standard:
Geometry (7, 8) / In addition to the Acceptable level, the unit integrates at least 2 other content strands. / Unit fully and accurately develops one of the Geometry standards in a logical, sequential manner. / Unit does not address a component of the NCTM Geometry content standard OR inaccurate content is included.
NCTM Standard:
Problem Solving
(3, 7) / In addition to the Acceptable level, a description of effective problem solving is provided. / Unit provides a plan for building new mathematical knowledge through problem solving and includes problem solving throughout. / Unit includes a minimal amount of problem solving.
NCTM Standard:
Reasoning and Proof
(5, 7) / In addition to the Acceptable level, a description of effective reasoning and proof is provided. / Unit requires students to make and investigate mathematical conjectures and requires student reasoning from all students. / Unit does not require all students to demonstrate reasoning.
NCTM Standard:
Communication
(3, 5, 7) / In addition to the Acceptable level, a description of effective communication is provided. / Unit requires all students to communicate their mathematical thinking and use the language of mathematics. / Unit does not require student communication about mathematical thinking.
NCTM Standard:
Connections
(5, 7) / In addition to the Acceptable level, students are required to explain the connection to previously learned mathematical ideas. / Unit includes opportunities for students to recognize connections among previously learned mathematical ideas and connections to contexts outside of mathematics. / Unit does not encourage connections to other concepts outside of the unit focus.
NCTM Standard:
Representation
(5, 7) / In addition to the Acceptable level, unit requires students to use multiple representations for at least 3 of the learning activities. / Unit provides opportunities for students to demonstrate various representations to organize, record, and communicate mathematical ideas. / Unit does not provide for an opportunity for students to demonstrate various representations of mathematical ideas.
*Explanations can be brief (75 – 100 words).