January 16, 2012. Foundations 30 topics: ◦ Demonstrate understanding of financial decision ◦ Demonstrate understanding of inductive and deductive reasoning.

Workshop 10, 20, 30January 16, 2012

Foundations 30 topics:◦ Demonstrate understanding of financial decision◦ Demonstrate understanding of inductive and deductive

reasoning including◦ Demonstrate understanding of set theory and its

applications.◦ Extend understanding of odds and probability.◦ Extend understanding of the probability of two events◦ Demonstrate understanding of combinatorics ◦ Demonstrate understanding of the representation and

analysis of ◦ Research and give a presentation of a current event or an

area of interest that requires data collection and analysis.

Where are we going

Pre-Calculus 30◦ Extend understanding of angles to angles in

standard position, expressed in degrees and radians.

◦ Demonstrate understanding of the unit circle and its relationship to the six trigonometric ratios for any angle in standard position

◦ Demonstrate understanding of the graphs of the primary trigonometric functions.

◦ Demonstrate understanding of first and second-degree trigonometric equations.

Where are we going

◦ Demonstrate understanding of trigonometric identities

◦ Demonstrate an understanding of operations on, and compositions of, functions.

◦ Extend understanding of transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, horizontal and vertical stretches.

◦ Demonstrate understanding of functions, relations, inverses and their related equations resulting from reflections

◦ Demonstrate an understanding of logarithms

◦ Demonstrate understanding of polynomials and polynomial functions of degree greater than 2

◦ Demonstrate understanding of radical and rational functions with restrictions on the domain.

◦ Demonstrate understanding of permutations, including the fundamental counting principle.

◦ Demonstrate understanding of combinations of elements, including the application to the binomial theorem.

Workplace & Apprenticeship 30◦ Analyze puzzles and games that involve logical

reasoning using problem-solving strategies.◦ Demonstrate concretely, pictorially and

symbolically an understanding of limitations of measuring instruments

◦ Solve problems that involve the sine law and cosine law, excluding the ambiguous case.

◦ Extend and apply understanding of the properties of triangles, quadrilaterals and regular polygons to solve problems

Where are we going

◦ Extend and apply understanding of transformations on 2-D shapes and 3-D objects

◦ Demonstrate understanding of options for acquiring a vehicle

◦ Explore and critique the viability of small business options

◦ Extend and apply understanding of linear relations ◦ Extend and apply understanding of measures of

central tendency to solve problems

◦ Demonstrate understanding of percentiles

◦ Extend and apply understanding of probability

Questions/Comments

Art Architecture

Nature

Angles/Lines

Exterior angles of a convex polygon

Can you find any in the artwork by Hanna Hoch?

Puzzles/reasoning/lines

Ongoing but deliberate process

Promote growth◦ Inform instruction as you reach for a goal.

Improve instruction◦ Information comes at a time so it can be used to guide

instruction Recognize accomplishment

◦ Evaluation can take place in many ways, blur the line between instruction and evaluation

Modify program◦ How well did the unit work in terms of achieving my goals of

student learning Van de Walle & Folk (2004)

Building Assessment into Instruction

purposeful use of assessment to promote learning

Increasing amount of assessment does not necessarily translate to increased learning

Assessment influences learning when teachers use it to comprehend the understanding and beliefs their students bring to the classroom and the chosen task

assessment must be clear and explicit and designed to fit the purpose

Assessment of learning◦ Justify the grades assigned, rank students, certify,

report

Assessment for learning◦ Makes students thinking visible, how they make

sense from their perspective

Assessment as learning◦ Student build capacity to evaluate and adapt their

own learning

https://www.teachingchannel.org/videos/my-favorite-no

Favorite No

Uncover student understandings and misunderstandings

Diagnostic assessment strategies

Assessment Probes

Conceptual versus procedural

When they understand they are able to use their knowledge with more flexibly

Understand and reach proficiency

Question student understanding of a learning target

Uncovering student understanding

Examining student work

Seeking links to cognitive research

Teaching implications

QUEST

Have student write about the patterns they saw

Allows for assessment of student understanding

Journals

Frog and toad

Quadratics

Comments/Questions

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