Double Accelerating Plan in Math

[QuantamMaster]

Hello All,

I am an 8th grader taking honors geometry at the high school. I am accelerated in math by one year, but it quickly got boring and I wanted to do honors algebra II. I took the test for geometry (midterm and final) and failed to pass. This was about 4 months ago. I am trying to double accelerate again so that I can take ap precalc/honors accelerated precalc as a freshman.

Do you guys have any advice for me? I have not been super confident lately so anything would help.

Thank you.

 

[jedishrfu]

Yes, don't learn things super fast, slow down and learn things deeply.

Courses taught in high school are introductory courses on any given subject. There is a lot of material you can read and use to solve problems and deepen your understanding. In the long run, it will serve you well.

Your textbook often covers a lot more than what the teacher will teach so go in and learn those areas too for the challenge. You can check with your teacher or find a favorite teacher that could help you understand these new untaught topics.

Check out either Khan Academy or MathIsPower4u.com. Both have extensive short 5-minute math videos on every conceivable problem.

Personally, I think you might like MathIsPower4u as their courses are ones for 1st year college. However, they also have extensive high-school-level videos.

Your strategy should be to go beyond what the teacher is teaching and learn from the teacher so you can ace the tests.

Some areas to consider:
- the history behind the math, who thought of it first, and what problems they were working on.
- when you see a formula ask yourself how might I prove it's true. When does it work and doesn't it work?

Some famous mathematicians that might come up in your studies:
- Euclid and his Elements and the infamous parallel postulate that led to new geometries
- Archimedes and his discovery of the equations for the volumes and surface areas of the cylinder and sphere
- Leonard Euler many contributions including the Euler Identity
- Carl Friedrich Gauss many contributions known as the Prince of Mathematics
- Isaac Newton and his Calculus
- George Cantor and his set theory, and notion of cardinality of sets ie countably infinite (integers and rational numbers) vs uncountably infinite (real numbers)
- Ramanujan many contributions in number theory, infinite series and modular forms

There are some books to look into:
- Jay Gullberg's book:

https://www.amazon.com/Mathematics-Birth-Numbers-Jan-Gullberg/dp/039304002X?tag=pfamazon01-20

- ET Bell Men of Mathematics is an older book that has inspired many modern mathematicians (some non-western mathematicians are missing aka Ramanujan and some stories are overly dramatized while the math is a bit light)

- Math 1001 by Elways covers many interesting areas of math with pithy paragraphs. I really liked this book a lot as it brought up a topic and then I could later search on wikipedia and other sites for deeper info.

Almost lastly, there are several great youtube channels on math:
- Numberphile - all types of interesting math topics
- 3brown1blue has some really great and I mean really great math videos
- Veritaseum a mix of science and math
- Mathologer all math

NOVA Great Math Mystery episode:


And the independent lens one on origami:


Eric Demaine appears later in the video. He uses origami in unique ways. There is a lot of math to unpack there.

LASTLY, there are some challenging math contests for you to check out, but you'll have to prepare yourself like an athlete by studying past tests and exploring other areas of math.

Contest Name  / For /   Focus
AMC (8, 10, 12)  /  Middle/High School  /  Problem-solving basics
Putnam Competition  /  Undergraduates  /  Advanced, rigorous math problems
International Mathematical Olympiad /   High School (Worldwide) /   Top-level problem-solving
AIME  /  AMC High Performers  /  Intermediate to advanced math
Math Kangaroo /   Grades 1–12 /   Logic and creative thinking
EGMO  /  Female High Schoolers /   Challenging, IMO-style problems
MathCounts /   Middle School (U.S.) /   Team and individual problem-solving
APMO  /  Asia-Pacific High School  /  Advanced Olympiad problems
Julia Robinson Festival /   K-12 Students  /  Fun, open-ended math exploration
Caribou Contest  /  Grades K–12 (Online)  /  Problem-solving and logic puzzles

I think I've thrown enough mud at the wall.

 

[jedishrfu]

Another good math history book:

https://www.amazon.com/history-math...David-Burton/dp/0697111962/?tag=pfamazon01-20

 

[gleem]

ET Bell Men of Mathematics is an older book that has inspired many modern mathematicians (some non-western mathematicians are missing aka Ramanujan and some stories are overly dramatized while the math is a bit light)

@jedishrfu gave great advice. I agree this would be a great time to spend reading the history of math. Once you get more into math you may be consumed with those subjects leaving no time for this type of study.

Another book by E T Bell Is "Mathematics Queen and Servant of Science". It goes a little deeper into fundamental math and the contribution of famous mathematicians and scientists. He notes that college courses miss the spirit of modern math. Bell noted that this is exemplified by the response of N.H. Able ( who died at 27) how he contributed so much to mathematics in a short time. He replied. "By studying the masters and not their pupils.".

Be patient and establish a sound foundation.

 

[CrysPhys]

I am an 8th grader taking honors geometry at the high school. I am accelerated in math by one year, but it quickly got boring and I wanted to do honors algebra II. I took the test for geometry (midterm and final) and failed to pass. This was about 4 months ago. I am trying to double accelerate again so that I can take ap precalc/honors accelerated precalc as a freshman.

You're too young to drive, but I'll assume you know enough about cars to understand the following analogy. Your starting point is Pt A, and your destination is Pt B. There's a single road connecting the two; it's full of twists and turns, and the speed limit is 25 mph. But you say to yourself, "Hey that's for average drivers; I'm waay above average! I want to reach Pt B in half the listed time, so I'll drive at 50 mph. No biggy."

Part way in, you lose control, skid off the road, and land in a ditch. Fortunately, you're not injured, and the car has only minor damage. You call a tow truck; they pull your car out of the ditch and back on the road. But now you're behind schedule. "No matter," you say to yourself, "I'll make up for lost time by completing the rest of the trip at 75 mph." In the words of Mr. Spock, "Is this logical?!"

 

[jedishrfu]

I knew a friend who had accelerated his math. He had a natural ability to understand high-level math. By eighth grade, he had completed all of high school math, i.e., algebra, geometry, and trigonometry, plus a smattering of other topics.

There were no AP or IB courses at the time, so the school district was on the hook to pay for him to attend math courses at a nearby liberal arts college. By twelfth grade, he had completed all of the undergraduate college math suitable for a math major, including partial differential equations and boundary value problems.

One anecdotal story happened when he attended a party of college students and one of them bragged about all the high level math they knew. My friend then as a high school student told him he too had studied those things and was studying something beyond that.

It was like a scene out of the Goodwill Hunting movie where Matt Damon embarrasses an upper classman reciting things from several economics texts and then saying he learned it all at the public library for the cost of a few late books.

My friend also scored high on the MAA contest and was part of a team that competed in England with British and Russian students. I don't know how he did but the US team got trounced.

In hindsight, it was mainly because our tests were multiple choice where you can sometime eliminate fake answers that then improves your odds of guessing the right answer on timed tests. In contrast, the British and Russians were skilled in fill in the blank test questions.

We lost touch when he went to college and when he returned he was different and no longer interested in math. He got married and became highly religious to the extreme and we could never connect again.

My suggestion is be smart in a different way, and develop a sense of looking deeply at things. In the long run, it will give you the gift of helping others with their math issues when you can explain complex things plainly to them.

 

[Muu9]

If you want to accelerate, register for the AP precalculus exam at the beginning of 9th grade, and make an agreement with the head of your math depar that if you get a 5, they let you take AP calculus BC sophomore year. If they require a WASC-accredited course, you can use mathacademy.com

If you just want a challenge, go through the art of problem solving geometry textbook.

 

[MidgetDwarf]

If you are in the US. Check to see if the state foots the bill for classes at the local community college/university.

At least in California, highschool students get classes for free at CC.

 

[CrysPhys]

If you are in the US. Check to see if the state foots the bill for classes at the local community college/university.

At least in California, highschool students get classes for free at CC.

But doesn't a student need to pass some prerequisite high school courses or some sort of placement exam to be admitted to such a college program?

 

[Rupert Roy]

@jedishrfu gave great advice. I agree this would be a great time to spend reading the history of math. Once you get more into math you may be consumed with those subjects leaving no time for this type of study.

Another book by E T Bell Is "Mathematics Queen and Servant of Science". It goes a little deeper into fundamental math and the contribution of famous mathematicians and scientists. He notes that college courses miss the spirit of modern math. Bell noted that this is exemplified by the response of N.H. Able ( who died at 27) how he contributed so much to mathematics in a short time. He replied. "By studying the masters and not their pupils.".

Be patient and establish a sound foundation.

For the record, the mathematicianwho died too young was N.H. Abel.

 

[Muu9]

But doesn't a student need to pass some prerequisite high school courses or some sort of placement exam to be admitted to such a college program?

Usually that would be the accuplacer, which can place students anywhere from remedial algebra to calculus.

 

[vela]

But doesn't a student need to pass some prerequisite high school courses or some sort of placement exam to be admitted to such a college program?

Back in my day, you could be admitted to a community college without needing any special permission as long as you were at least 16 years old. I didn't have to take a placement exam back then, but these days, math departments typically use one to determine which class you should start in.

 

[CrysPhys]

Usually that would be the accuplacer, which can place students anywhere from remedial algebra to calculus.

Back in my day, you could be admitted to a community college without needing any special permission as long as you were at least 16 years old. I didn't have to take a placement exam back then, but these days, math departments typically use one to determine which class you should start in.

I would have thought that a student would be eligible to take classes at a community college only if they had exhausted the course offerings at their high school. E.g., if the student passed or placed out of pre-calculus, and the high school offered calculus, then the student would take calculus in high school. If the high school did not offer calculus, the student could then take it in a community college. Is that not the case?

Regardless, am I the only one here who finds the following to be a red flag?

I am accelerated in math by one year, but it quickly got boring and I wanted to do honors algebra II. I took the test for geometry (midterm and final) and failed to pass.

<<Emphasis added.>> I realize there is debate about how useful a gauge certain tests are. But realistically, if a student is to advance academically, they typically (excluding outliers) need to pass tests to prove proficiency at one level before progressing to the next. The OP is in eighth grade. Given their performance so far, I would think that considering community college courses as an option is premature, to put it diplomatically.

 

[vela]

Regardless, am I the only one here who finds the following to be a red flag?

Nope. I wonder what the OP found so boring about geometry. I kind of suspect he dislikes the material because it's not like "regular math," i.e., algebra and trig.

In any case, the OP hasn't been back since the first post, so this is probably just a drive-by thread.

 

[jedishrfu]

We all see this red flag. That's why we've been encouraging the OP to slow down and learn more deeply.

In my experience, there is low-hanging fruit in learning Calculus. The rules are straightforward to apply to get derivatives and understanding what a derivative is or what an integral is give you some measure of useful knowledge.

It helped me get past the Calculus I course in college and into Calculus II speeding me along to introductory physics. But in the process I missed a few things like how to apply the knowledge in other areas that would have helped later on.

So yes, we saw the red flag and advised the OP on the value of learning the material more deeply. It's the journey not the destination that is more meaningful.

 

[QuantamMaster]

Hello everyone,

I was extremely busy these past few days as I was studying and taking a midterm for my geometry class. Thank you guys so much for the kind and inspiring words you have given me as well as the resources.

I would have thought that a student would be eligible to take classes at a community college only if they had exhausted the course offerings at their high school. E.g., if the student passed or placed out of pre-calculus, and the high school offered calculus, then the student would take calculus in high school. If the high school did not offer calculus, the student could then take it in a community college. Is that not the case?

Regardless, am I the only one here who finds the following to be a red flag?



<<Emphasis added.>> I realize there is debate about how useful a gauge certain tests are. But realistically, if a student is to advance academically, they typically (excluding outliers) need to pass tests to prove proficiency at one level before progressing to the next. The OP is in eighth grade. Given their performance so far, I would think that considering community college courses as an option is premature, to put it diplomatically.

Yeah I did fail that test, but that was only because I actually did not study and do and learn the proofs that they gave properly, and the reasons of those proofs. I now know the proofs better, and I have also learned a lot of things outside of geometry, and algebra II. I have done Khan Academy on those courses and finished, and am confident in those courses now.

 

[jedishrfu]

That's great!

Have you looked at the MathIsPower4U.com videos?

They cover even more topics than Khan Academy.

 

[QuantamMaster]

Yeah I have watched three of their videos so far, and they explain it better. Thanks for the amazing resource!