Quiz #1
Name:
CI-448 Teaching Children Mathematics
1. What is the role of the “Vision” paragraph in regards to the rest of the Principles and Standards? Give three key ideas contained in that section.
Here most of you did well. The key ideas are (these were mostly discussed in class):
• This paragraph represents the “ideal” math classroom environment, in terms of what mathematics is important, how students learn, and what is most e ff ective teaching.
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It also emphasizes a ff ective issues, equity issues, appropriate use of technology, and
It previews the 6 principles: curriculum, assessment, teaching, technology, learning and equity.
2. What are the process standards? Name them and explain what they mean.
Some of you confused these with the Principles (listed above). The process standards are (this is found on page 4 of the text):
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Problem Solving: here the document talks about teaching THROUGH problem solving, or problem solving as the main vehicle for learning,
Reasoning and Proof: this one emphasizes the logical thinking that students must show as they justify their work.
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Communication: Sts must be able to talk, describe and write about their mathematical ideas.
Connections: relates to connections among di ff erent math ideas, and connections between math and every day life.
Representation: is the ability of sts to use symbols, charts, manipulatives, software, etc, to express their ideas. Sts should be able to translate between these di ff erent media.
3. Which content areas are covered by the Iowa Core Curriculum? What connections do you see between the Iowa Core
Curriculum and the NCTM’s Principles and Standards?
Here again, most of you did quite well. I didn’t ask the question as clearly as I wanted to so there are a couple of possible ways to answer the first question. I wanted you to tell me (and to know) that the Iowa

Quiz #1
CI-448 Teaching Children Mathematics
Core Curriculum covers more that just math, so I expected most of you to answer: Math, Science, Social Studies, and 21st Century Skills.
Some of you thought I meant what were the Content Standards for Math only according to the ICC, and those are (for K-8): Number and Operation, Algebra, Geometry and Measurement, and Data
Analysis and Probability.
I accepted both version of that answer as correct.
For the second part of the question, the main idea is to relate how closely the ICC follows the ideas of the NCTM Principles and Standards.
All of the above comes from the PowerPoint, the class discussion, and the website we looked at in class
(www.corecurriculum,iowa.gov.)
4.What are relational and instrumental understanding? Use examples from school mathematics to elaborate on your explanations.
Most of you did well. The material for this comes from pp. 23-24.
Understanding can be measured by the number and the strength of the connections between ideas. The more connections, and the stronger they are, results in RELATIONAL understanding, which is the goal for our students.
If an idea is known in isolation, with few connections to other mathematics, we call the understanding
INSTRUMENTAL.
Most understanding lies between these two poles.
There is a good example in the text relating to fractions that you might want to check out, though again most of you did well. I did ask for an example, and almost everyone provided one.
5. Give examples that describe the di ff erences between learning about, for, and through problem solving.
Here there was some confusion for many of you. THIS IS IMPORTANT, so make sure you understand it.
Teaching for problem solving is when you first learn some mathematical content, and then you are asked to apply this learning to a story problem situation. I’m sure you can recall situations in High School when you were taught how to use the Pythagorean Theorem, and then you were given some (dopey) exercise involving a wall and a ladder, and you had to figure out how high up the wall the ladder went.

Quiz #1
CI-448 Teaching Children Mathematics
Teaching about problem solving is when you learn specific techniques to become a better problem solver, like the 4 steps we discussed in class.
Teaching through problem solving is the key of the Principles and Standards and of the Iowa Core Curriculum, and it involves having students learn mathematical content THROUGH their solving realistic and context-appropriates tasks. The video of the CGI classroom we watched in class is one such good example.
All of the above can be found on p. 32.
6. What are the requirements for a good task or problem?
Most of you missed some ideas here. They are all in page 33. Notice how well the requirements below go with the before-during-after lesson plan format. Here they are:
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7. Give 3 benefits of learning through problem solving.
These are all in p. 34, and in one of the slides I sent. Here are some, you only needed 3, and I tried to be generous. If you had something similar or even reasonable, I gave you the points.
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The problem must begin where sts are. In other words most if not all students should be able to engage in the problem, yet find it challenging and interesting.
The problematic aspect of the task must be due your mathematical goal for the lesson, and
The students are responsible for explanations and justifications.
focuses sts’ attention on making sense of the mathematics, develops confidence in the sts that they can make sense of the mathematics, and their ability to do mathematics in general, provides (through the task/story problem) a context to relate the mathematics to, allows an entry point for a wide range of students, provides ongoing assessment data, develops “mathematical power”, among others.

Quiz #1
CI-448 Teaching Children Mathematics
8. Describe what should happen in each stage of the three phase lesson format.
All of you got this right, and it’s on pp. 48-54 (and I think in one of the slides I emailed). The basic idea:
Before: Evoke the right prerequisite knowledge and skills, motivate the task, and maybe do a smaller version of the problem, or have sts estimate the solution.
During: You let go. Let sts work on the problem, provide guidance were needed (if possible, in the form of questions), assess sts’ progress, and plan the discussion to come in the...
After part: Here let students discuss their solution. Map the discussion so as to emphasize the ideas and skills that were your mathematical goal.