To answer the questions effectively, consult our textbook, your class notes, the internet (not AI), and your own work. It would be best if you made references (i.e.: textbook, website, r presentation name, page numbers from books, paragraphs on websites, title of slides and slide number, etc.) when using information from these places.
I have attached all the notes and some slide decks and the text book used for the class Elementary and Middle School Mathematics, Canadian Edition, 6th edition
Published by Pearson Canada (July 12, 2021) © 2022
John A. Van de Walle Virginia Commonwealth UniversityKaren S. Karp Johns Hopkins UniversityJennifer M. Bay-Williams University of LouisvilleLynn M. McGarvey University of Alberta
Please consider being a kindergarten teacher to answer these questions and keep in mind the Canadian BC curriculum.
Here are the questions!
Question 1:
Tom Romberg makes an analogy between music and mathematics. In music, there is a relatively limited notational system of notes and lines on paper. There are also 13 musical theories that involve the structure of scales and harmonies and rules for composition. Many excellent musicians study this theory and have learned this notation. “However,” Romberg says, “no matter how many of the artifacts of music one has learned, it is not the same as doing music.”
Geraldine Brooks has said, “A book is more than the sum of its materials. It is an artifact of the human mind and hand.” There are mechanics of writing to consider when creating a piece of writing, the elements of a story one must include, and the storyline that can be created or retold. However, even if the author learns all these parts of creating a story, it is not the same as creating a story that captures the human heart and mind.
The author of the site, Fred Astaire Dance Studios (Fred Astaire Dance Studios Bloomfield Hills | Dance Lessons & Classes | Bloomfield Hills), wrote a post on the connection between dance and doing dance. In dance, many people believe that it is just a series of steps—learn the steps, have your partner learn the steps, then you can dance! Many excellent dancers study the theory and have learned the steps. While dance is a sequential order of steps, the author feels it is so much more! You have to learn EVERY part of dance! It involves emotion, drama, acting, and presentation.
The quote: Dancing is more than just learning steps. I always tell people, “You can learn steps. You can go online, watch YouTube, buy a book, but that’s not going to make you a dancer.” So, no matter how many of the artifacts of dance one has learned, it is not the same as doing the dancing. It goes on to say: “The connection is everything.”
Briefly explain how these example stories relate to mathematics, as it applies to what we have discussed in this course as best practice for teaching and learning math and the design and structure of BC’s Mathematics curriculum. Be sure to make at least one reference to one of the above small stories and one reference to the BC Curriculum website to support your explanation.
Question 2:
Make the number 327 with your base 10 materials. One way to do this requires exactly 12 pieces. Can you show 327 with 28 pieces? Why or why not? Is there more than one way to do that? What else can you find out about ways to show 327?
Suppose that you were to use this above task with a group of Grade 3 children. Describe some things you would do in each of the following three phases of teaching: Introduction, Development (Disclosure and Practice), and Closure.
Question 3: (choose one)
Make a list of different forms of communication that are necessary and used in the teaching and learning of mathematics. Then, include all the reasons you can think of that lend support to the idea that different forms of communication in math facilitate understanding and learning. Be sure to reference your ideas as needed.
OR
A parent has challenged you about the validity of teaching math using inquiry strategies vs. using traditional methods. Create a chart, or similar method for comparison, which explains the pros and cons/benefits and drawbacks of both methods. Then, justify how you would employ inquiry in your classroom. Be sure to reference your ideas as needed.
Question 4:
David is attempting to use percents to try and explain why ½, 2/4, and 3/5 are the same. He figured out that 3/5 is 60 percent. He also soon realizes that ½ is 50 percent.
“Is ½, 2/4, and 3/5 the same? So, where would you put 3/5 on this line?” the teacher asks.
“Hmmm,” David replies, “this is hard.”
The teacher suggests using colour tiles, fraction bars, and a number line to see if this can support David’s thinking.
David’s responses indicate that his understanding is partial at this point. The teacher suggested using colour tiles and fraction bards because he thought David’s ability to reason spatially was stronger than his ability to reason with the numerals or the number line model. The teacher is always looking for ways to help students move from their stretches (weaknesses) to strengths. The teacher sees value in letting students explore different possibilities and use inquiry to learn. Many teachers are often hesitant about this, preferring students to follow their line of reasoning (or that outlined in a textbook) rather than letting students struggle with finding their own way.
Thinking about this scenario, answer the following three questions:
What do you think about a teacher’s attempt to link David’s spatial understanding and reasoning through colour tiles or fraction bars (using concrete examples of fractions and percentages) in order to compare 2/4 and ½ and 3/5 on the number line (putting it into a more abstract form on a number line)?
What would you do at this point?
What is the role of confusion/allowing students to struggle in student learning?
Question 5:
To learn about place value, children benefit from a variety of experiences. According to the textbook, they should estimate and count large numbers of objects, work with concrete materials, draw/make pictures of their thinking, relate our number system to money, look for patterns in written numbers, and explore numbers in everyday contexts.
How might a teacher help students be engaged in activities that require them to compare the sizes of numbers and think about the logic of numerical symbols, as they relate to place value? Note: If it helps, you may choose to specify a grade level to focus on.
OR
Canada uses the metric system for measurement, and items sold in Canada need to be labeled using metric units. Students learn this in 3 steps:
1. making comparisons
2. using models of measuring units
3. using measuring instruments
Briefly explain an activity for each step of learning that follows a particular theme/cross-curricular theme. Include key vocabulary needed, manipulatives/tools needed for the activity, possible misconceptions, and ways of knowing the student has learned or mastered the step.
Question 6:
Clearly and thoroughly describe a problem-solving activity that children could do independently of the teacher while working in pairs. For example, if the teacher is leading a small group centre, what could students be doing at another centre in pairs that involve problem-solving?
When thinking of an activity, keep in mind that the activity should not be entirely symbolic, but there should be counters or other manipulatives involved. There should also be an oral component to the activity as the two children work together. Be sure to describe and cite any activities that you might use if necessary.