Daniel Bochicchio Neag School of Education

Tell us a bit about yourself Why do you want to teach math? What do you want to learn about teaching math?

 Describe the work you’ve done in your previous classes.  What piece of work so far are you most proud of?

 Class Topics  Course Assignments

 Equity  Curriculum  Teaching  Learning  Assessment  Technology

 High expectations and worthwhile opportunities for all.  Accommodating differences to help everyone learn mathematics.

 Be coherent  Focus on important mathematics  Well articulated across the grades.

 Knowing and understanding mathematics, students as learners, and pedagogical strategies.  A challenging and supportive classroom learning environment.  Continually seeking improvement

 Allow students to understand.  Actively build new knowledge from experience and prior knowledge.

 Enhance students’ learning.  Be a valuable tool for making instructional decisions.  Furnish useful information to students.

 Enhances mathematics learning.  Supports effective mathematics teaching.  Influences what mathematics is taught.

 Number and Operations  Algebra  Geometry  Measurement  Data Analysis and Probability

 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.  Understand meanings of operations and how they relate to one another.  Compute fluently and make reasonable estimates.

 Understand patterns, relations, and functions.  Represent and analyze mathematical situations and structures using algebraic symbols.  Use mathematical models to represent and understand quantitative relationships.  Analyze change in various contexts.

 Analyze characteristics and properties of 2- and 3-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.  Apply appropriate techniques, tools, and formulas to determine measurements.

 Select and use appropriate statistical methods to analyze data.  Develop and evaluate inferences and predictions that are based on data.  Understand and apply basic concepts of probability.

 Problem Solving  Reasoning and Proof  Communication  Connections  Representation

 Build new mathematical knowledge through problem solving.  Solve problems that arise in mathematics and in other contexts.  Apply and adapt a variety of appropriate strategies to solve problems.  Monitor and reflect on the process of mathematical problem solving.

 Recognize reasoning and proof as fundamental aspects of mathematics.  Make and investigate mathematical conjectures.  Develop and evaluate mathematical arguments and proofs.  Select and use various types of reasoning and methods of proof.

 Organize and consolidate their mathematical thinking through communication.  Communicate their mathematical thinking coherently to peers, teachers, and others.  Analyze and evaluate the mathematical thinking and strategies of others.  Use the language of mathematics to express mathematical ideas precisely.

 Recognize and use connections among mathematical ideas.  Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.  Recognize and apply mathematics in contexts outside of mathematics.

 Create and use representations to organize, record, and communicate mathematical ideas.  Select, apply, and translate among mathematical representations to solve problems.  Use representations to model and interpret physical, social, and mathematical phenomena.

DERG A DERG I From to

 Be coherent  Focus on important mathematics  Well articulated across the grades.

 Design authentic learning experiences that integrate skills and knowledge.  Use different types of instruction to teach skills and knowledge.  Develop fluency through variation within lessons.  Organize instruction into patterns for maximum effectiveness.  Teach a range of skills and types of knowledge.

 Embed skills and knowledge instruction within context of an authentic, purposeful assignment.  Have students identify and solve problems they encounter in the context of their work by teaching them the steps in the problem solving process.  Organize the learning experience around essential questions that drive inquiry.  Ask yourself, “What do I want students to know?”.  Use context-rich activities such as simulations, case studies, performances, investigations, projects, and productions.

 Add complexity as students begin to show initial mastery.  Vary the means and materials students use.  Vary the duration of the activity or assignment.  Support your students in a variety of ways.

 Ask yourself what skills, of any type, are necessary to do what you ask.  Model and incorporate different types of skills for students.  Monitor the skills and knowledge you have taught.  Post certain declarative and procedural knowledge.  Move beyond basic knowledge into advanced critical thinking.

 Standards  Content  Essential Understanding/Questions  Performance Outcomes  Instructional Tools/Methods  Assessments

 Cause genuine and relevant inquiry into the big ideas and core content.  Provoke deep thought, lively discussion, sustained inquiry, new understanding, and more questions.  Create opportunities for transfer to other situations and subjects.  Require students to consider alternatives, weigh evidence, support their ideas, and justify their answers.

 How is trigonometry used to solve real world problems in engineering and science?  How does knowing the basic trigonometric ratios simplify finding distances and angles?  What project have you or your family done, or plan to do, that might involve trigonometry?

Angles And Degree Measurement  Determine the length of the sides of a right-triangle using the Pythagorean Theorem.  Measure and identify positive and negative angles using a protractor.  Indicate the number of degrees in an angle formed by rotating the terminal side.  Convert an angle measurement in a decimal degree to degrees-minutes-seconds and vice versa. Similar Triangles  Determine if two triangles are similar.  Find the lengths of unknown sides in similar triangles.  Use the relationships in a triangle to find the lengths of unknown sides.  Use the relationships in a triangle to find the lengths of unknown sides. Trigonometric Ratios  Calculate the value of trigonometric functions for a given triangle.  Evaluate trigonometric functions using a calculator.  Solve a right triangle using trigonometric ratios.  Evaluate inverse trigonometric functions using a calculator. Right-Triangle Applications  Use trigonometric ratios to find the angle of elevation and the angle of depression.  Use trigonometric ratios to find inaccessible distances. Angles And Arc Length  Draw an angle in standard position.  Find an angle coterminal to a given angle.  Find the reference angle of a given angle.  Find the length of an intercepted arc when given the central angle and the radius.  Find the value of a central angle when given an arc length and a radius.

Angles And Degree Measurement  Class discussion  Presentation  Paired activity - Pythagoras ' Pool  Paired activity - What Goes Around?  Dance - The Trig Angle Dance  Activity - Going Back And Forth Similar Triangles  Class discussion  Presentation  Project - Height Of An Object Using Mirrors And Shadows Trigonometric Ratios  Class discussion  Presentation  Activity - The Tangent Ratio  Activity - Creating The Trig Table  Paired activity - Building A Ramp To OSHA Standards Right-Triangle Applications  Class discussion  Presentation  Activity- Coming In For A Landing  Paired activity - Finding The Impossible Angles And Arc Length  Class discussion  Presentation  Activity- What's Your Position?  Activity - Check Your References  Paired activity - Measuring The Globe  Cumulative project - Using A Clinometer To Measure Heights

 Written results  Informal observations  Activity results  Written activity results  Oral questioning  Completed worksheet  Student responses  Written responses  Completed lab worksheet  Project rubric  Test on right-triangle trigonometry

Select a unit of study  What are your essential questions?  What content will you teach?  What are your performance outcomes for the unit?