1. Sibley, Brown-Shuford worked with continuous choices on or in an
equilateral triangle. Replace a discrete thirteen-element system Figure 1 by a two-stage process that allows choice
of either of these responses. Stage 1: ? - response equidistant to three
vertices; any vertex; or slider on two vertices. Stage 2: scored value
based on slider location between the two vertices chosen.

2. Sequential training. Many responses in questions with three possible
answers lead to other questions. .
Develop a sequence of linked questions leading to deep understanding of a
topic. Examples could be in math concepts like odd/even, math-induction
or probability. See Illustrative Sequential Example below

### Illustrative Sequential Example

1. Both 2x2x2 and 3x3x3 are easily expressed as the sum of adjacent odd
numbers. Which statement is true?

a) Two and three are unique in this regard.

b) Representing 21^3 by the sum of adjacent odd numbers must include 19,
21 and 23.

c) Neither a) nor b).

CORRECT ANSWER is c). [Since the understanding
of the topic requires distinguishing odd from even, c) leads to question
2.]

2. Nine apples are to be placed in four baskets so there is an odd
number in each (zero is even; apples can't be divided/cut).

a) This is clearly impossible.

b) Neither a) nor c).

c) Three baskets have to hold three apples while another contains one.

CORRECT ANSWER is c). [Since stacking baskets isn't disallowed. This choice
leads to question 3. about hierarchy.]

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