Self-study
The graphical illustrations mathematics teachers use enable students to learn geometry more easily by providing them with an intuitive understanding of geometric concepts, which makes it easier to acquire the ability to manipulate symbols for the purpose of calculation. ████████████ █████████ ████████ ███████████ █████ ██ ███████ █████████ ██████████████ ████ ██████ ███ ███████ ████████████ █████████████ ██ █████████ ███ ██████████
Summary
Teachers enable students to learn geometry more easily by using graphical illustrations. This is because the illustrations provide students with an intuitive understanding of geometric concepts, which makes it easier to manipulate symbols. Graphically illustrating algebraic concepts would be equally effective, even though the deepest mathematical understanding is abstract.
Strongly Supported Conclusions
This is an “except” question and any strongly supported conclusion would be an incorrect answer. We’re looking for an answer that is unsupported or least supported. Some strongly supported conclusions could be:
Imagistic understanding is not the deepest level of mathematical understanding.
Some teaching strategies can be used to teach students both geometric and algebraic concepts.
Graphically illustrating geometric concepts is an effective teaching strategy.
1.
The statements above provide some ███████ ███ ████ ██ ███ █████████ ███████
a
Pictorial understanding is ███ ███ █████ █████ ██ ████████████ ██████████████
This answer is strongly supported. We know from the stimulus that the deepest level, and therefore final stage, of mathematical understanding is abstract.
b
People who are ████ ████ ██ ████████████ ███████ ██ ███ ███████████ ████ ███ ████████████ ██████████████
This answer is unsupported. We know from the stimulus that there are some people who are both good at manipulating symbols and have mathematical understanding. We don’t know if there are some people good at manipulating symbols but don’t have mathematical understanding.
c
Illustrating geometric concepts ███████████ ██ ██ █████████ ████████ ███████
This answer is strongly supported. We know that graphically illustrating these concepts is an effective teaching method from the first sentence.
d
Acquiring the ability ██ ██████████ ███████ ██ ████ ██ ███ ███████ ██ ████████ █████████
This answer is strongly supported. We know that this process is involved in learning geometry from the first sentence.
e
There are strategies ████ ███ ██ ███████████ ████████ ██ ███ ████████ ████ ██ ███████ ███ ██ █████████
This answer is strongly supported. We know this because the stimulus tells us that using graphic illustrations would be “equally effective” for teaching algebraic concepts.