Tag Archives: math

New Changes to Math Curriculum in California

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The proposed mathematics framework in California has placed a heavy emphasis on equity in the teaching of math. The document makes several statements to support this, such as the following.

“All students are capable of making these contributions and achieving these abilities at the highest levels,”

In other words, all students can experience success in mathematics. Living in a subjective world of “lived experiences,” this statement does not appear to make sense alone. However, the document goes on to state that.

“We reject ideas of natural gifts and talents.”

Again this does not make sense. The world is full of highly talented people who obviously have superior abilities. Pick any field or industry, and you can find an Einstein, Newton, Mozart, Bach, Keynes, Shakespeare, or others. To reject natural gifts and talents is almost akin to dismissing reality.

The goal of the mathematics framework is summarized as follows

“to replace ideas of innate mathematics ‘talent’ and ‘giftedness’ with the recognition that every student is on a growth pathway.”

All students are indeed on their own “growth pathway” but given that there are differences in all students, it implies that the growth will be different. There is no such nonsense found in sports. Nobody will say everyone can play basketball at the highest level and that nobody has a natural talent at basketball. Playing professional basketball requires at the minimum unusual height and a plethora of other skills that can be partially developed. If someone is under six feet tall, it will be a long road to professional sports, even with supreme talent.

Athletes also receive special training and classes as it becomes apparent that they have potential. If someone can demonstrate superior athletic ability, is it not possible for someone to demonstrate exceptional mathematical ability and thus the need for specialized training and development?

The framework also disagrees with such ideas as

  • Finding the correct answer
  • Showing your work
  • Individual practice

Finding the correct answer is critical for anybody who wants to work in a math focus field. Who would feel comfortable flying in a plane designed by an engineer who was not worried about getting the “correct” answer? Showing your work helps students understand what they are doing and allows the teacher to see where mistakes were made and how to intervene. Again, who would want to go into surgery with a doctor who cannot explain what they will do? Lastly, individual practice means that the student can do the work and does not lean on friends.

Not allowing students to grow and demonstrate their innate talent and abilities is crippling for them. All students need to be challenged and pushed but how this is done depends on the students. All students have talent in something, and schools should helping students determine what they excel at and how to survive what they are weak at. Nobody excels at everything, and nobody fails at everything either.

Transversals: VIDEO

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Transversals are one of many mathematical concepts that students learn in geometry. Although they can seem mysterious this is a foundational idea that reappears in higher level mathematics. We will learn about interior/exterior angles corresponding angles and so much more in this video.

Regular Polygons: VIDEO

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This video will show you how to calculate the degrees of each angle inside a polygon. The calculation is not too complicated and this is commonly taught to high school students who are studying geometry. Mastery of this concept can help with learning other ideas.

Angle Types: VIDEO

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Understanding the various angle types is important in geometry. At first, this is confusing, however, with time this becomes easier. This is important because completing more advanced analysis requires that identifying angle types is automatic for the student. Often, the only way to make this easier is through practice. In the video below, we will learn about various angle types.

Lines and More in Geometry VIDEO

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Perpendicular & Parallel lines are basic ideas found in geometry. The video below explains the various types of lines a student will encounter in geometry. Some of the ideas discussed include parallel lines, perpendicular lines, midpoints, bisectors, etc. Be sure to leave a comment about the video below.

Set Symbolism: VIDEO

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Set Symbolism is important. In the video below it is introduced in the context of geometry but set symbolism is also used when talking about probability. It can be hard to appreciate learning this at times but it is useful in certain situations.

Planes in Geometry: VIDEO

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Planes are two-dimensional shapes. Planes geometry involves the analysis of two-dimensional shapes. In the video below, these ideas are explained in greater detail. Please comment or like the video and let us know how we can improve things.

Area Under the Curve: Right Endpoint VIDEO

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The video below shows how to calculate Area Under the Curve with the Right Endpoint. This is one of several ways to find the area under the curve. Leave a like and or a comment so we know how we can improve.

Area Under the Curve: Left End-Point VIDEO

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Calculating the area under curve is one of those ideas in calculus that can be challenging. In the video found below, we will learn how to calculate the Area Under the Curve using the Left End-Point. This is one of several ways to do this but needs to be learned in many calculus courses.

Instantaneous Rate of Change VIDEO

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Instantaneous rate of change is the topic of this video. The ideas discussed here lay the foundation for more complex ideas related to derivatives. After watching the video, be sure to like and leave a comment.

Average Rate of Change VIDEO

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In this video that deals with the Average rate of change we will learn how to calculate this in a simple way. Videos like these are for students who may still be studying mathematics. Be sure to like and leave a comment.

Function of Limits: Exponents & Quotients VIDEO

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Function of Limits: Exponents & Quotients

One & Two-Sided Limits VIDEO

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One & Two-Sided Limits are discussed in detail in this video. Be sure to like and comment after watching. Doing so helps us to improve our services

Intro to Limits VIDEO

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Limits are another concept in math that leads to something even more complex in terms of derivatives. In the video below the idea of limits is discussed from a practical and simple perspective. Be sure to like and comment on the video after watching.

Probability & the Union of Two Events VIDEO

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Probability & the Union of Two Events

Combination Formula for n Distinct Objects VIDEO

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Combination formula for n distinct objects

Formula for Permutations & n Distinct Objects VIDEO

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Formula for Permutations & n Distinct Objects

Permutations & Multiplication Principle VIDEO

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Permutations & Multiplication Principle

Geometric Sequences: Recursive Formula VIDEO

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Geometric Sequences: Recursive Formula


Arithmetic Sequences: Finding the Number of Terms VIDEO

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Arithmetic Sequences: Finding the Number of Terms

Arithmetic Sequences: Finding the nth Term of an Explicit Formula VIDEO

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Arithmetic Sequences and Finding the nth Term of an Explicit Formula