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Reflection on this class and what I have learned

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Big Ideas:

1.       Using correct vocabulary early on to build off of in later grades.

2.       Using different models and manipulatives for fractions.

3.       How to properly integrate geometry in early grades to avoid later confusion.

2 Questions:

How many statistic questions are on map testing and other standardized tests? In my elementary school only a few questions were related to statistics so it was never focused in school therefore it was challenging for me in high school.

Should students already be comfortable with multiplication and division before teaching past the basics of fractions?

Aha-moment
Kindergarten class is already using statistics by counting the number of students who like answer a vs. answer b and finding which answer has the most or “more than.” I never realized this is integration of statistics early on.

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3 Big Ideas

The process of measuring includes deciding what to measure, selecting an appropriate unit, and comparing the units.

How to introduce the standard unit smoothly.

Guessing units should be focused on finding the exact answer and not about who can guess the best.

2 Questions

Would having a lot of examples of objects measured that would benefit with a smaller unit be a great way to introduce using smaller units/multiple?

How much time should be spent on reading clocks? I feel like reading clocks are a lot less prioritized with everything being digital. The only time I see clocks with faces are in classrooms.

Aha-moment

Relationship of area and perimeter and weight/mass reminds me of addition/subtraction and multiplication/division. Need to be taught together. Math is all connected and needs to be taught this way.

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3 Big Ideas
1. Models and representations are a great way to learn multiplication and division.

2.  Lots of strategies for solving multiplication and division that should be taught or shown to students for solving equations efficiently.

3.  You can make connections to reading by using books to teach multiplication and division.

2 Wonders

When do we move on from models? Is it something we continue to ask students?

What are some common errors in teaching multiplication and division teachers need to look out for?

Aha-moment

I have never seen fair trade for division. My division learning was not the strongest. This was really interesting to see.

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3 Big Ideas

Teach math symbols correctly by using careful language and a variety.

Four types of addition and subtraction problems: join, separate, part-part-whole, and compare.

Teach multiplication with division soon after to help students connect the two ideas. (same principles apply with symbols and contextual problems)

2 Questions

Do you have students identify the equation type? (Like join or compare.)

I worked with a student who did not understand the concept of zero at all even when providing contextual problems. How would I go about this? Would showing patterns in equations help more?

1 Ah-ha

I did not know previously that multiplication/divisions had four categories of problems like addition/subtraction: equal groups, comparison problems, array, and combination problems. I can see connections with addition/subtraction in the format and similarities in teaching concepts.

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3 Big Ideas

1.Place values have meaning and there are three levels for understanding this.

2.Teach with things you can bundle to teach place value

3. Create real world connections with place value and bundling

2 Wonders

1.Could you go back and forth between base-ten language in older grades? Would this be a good refresher?

2.Would teaching a place value song along with teaching the concept of place values be acceptable?

AHA-Moment

Using base-ten language before transitioning into standards to make sure students understand place value location. Make sure to talk about teens as an exception to the pattern (are backwards language).

(My allergies were bad when filming this. I apologize for all the coughing, haha!)

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3 Big Ideas

1. Subitizing

2. Learning trajectory levels

3. Games for formative assessment

2 Wonders

1.   What do you do if a student did not meet all the learning trajectory steps and is in a higher grade level? Best steps to approach as a teacher?
2. Does it matter what order you implement concepts? Five-frame was used in my kindergarten class, but more/same/less has not been.

Aha moment- Graphs connecting to students to interpret. I remember doing this in school and finding it so fun and being heavily engaged.

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3 Big Takeaways

1.Teaching through problem-solving uses a 3phase structure for lessons

2. Importance of culturally relevant teaching in math

3. Modeling is important

2 Wonders

1. If teachers often confuse students’ work for not being enough due to cultural barriers?

2. How would you go about some students finishing a task early and other students not, without making it noticeable? How would you naturally challenge the students who typically finish tasks earlier?

1 Aha-moment

Culture has a huge impact on how students do math. It made me realize that if I do not understand this it could cause me to evaluate the math poorly (thinking students are not solving the math and just guessing).

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3 Big Takeaways

1.       Memorization is ineffective

2.       Phases of mastery and how to achieve it

3.       Games over drills

2 Wonders

1. Why was memorization a common practice of teaching math when I was a student?

2. Can memorization tactics still be a useful practice in the classroom? Like songs to recall basic math facts while still teaching the reasoning behind the fact?

Aha Moment

My aha-moment was the make whole strategy with adding 1 to 9 then removing it after adding. I have done this before on my own but I was never taught this simple strategy in school. A lot more effective than remembering addition facts.

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Big Takeaways- Make math feel important (because it is)
Understand the topic not just how to solve an equation

Teacher pulling the strings (behind scenes)

2 Wonders

1. I wonder if there are ways to get students to create the formula. How to set students up to find a formula on their own instead of giving it to them?

2. I wonder if there are effective ways to bring other subjects into math to improve problem-solving and benefit students in the real-world. What are some examples to do this?

AHA MOMENT

(Aha moment) Patient problem-solving – I realized I want to solve questions very fast and I do not want to think about the how, why, or the process. Typical word math questions are setting up for failure in real-life math problem-solving because they provide a quick way to solve the answer. Teachers have to reshape word problems to ask a question that engages and interests students first instead of providing step-by-step to solve.