Removing Taylor series was a tough call. It's one of my favorite calculus topics topics. Something had to give. However, those topics will still serve as prerequisite material for courses that explicitly need them.
Hi, I'm Alex, curriculum director at Math Academy.
Thanks for your comments. In response to the things you'd like us to have:
"ability to skip lessons" - we plan on introducing "mini-diagnostics" sometime soon, hopefully within the next few months. This will allow students to "place out" of certain content they know. The primary diagnostic assessment will have done most of the grunt work here, but mini-diagnostics can be used for fine-tuning the knowledge frontier.
"a reference page to track unlocked material" - This is an interesting idea that we can discuss.
"fewer multiple choice questions" - We're actively introducing "Free Response" across the entire curriculum. Complete coverage across all courses will likely take several months, maybe over one year. Many of our lower-grade students should be seeing lots of free-response questions already.
"more in-depth problems" - we have multipart problems in most courses. We plan to add many more. Introducing "challenge problems" into the curriculum is also something we have planned for the near future.
"proof-based math" - We plan on launching our "Methods of Proof" course within the next 6-8 weeks. This course is designed to introduce students to all fundamental concepts related to proof building: sets, logic, functions, relations, cardinality, proof by induction, direct proofs, counterexample, contrapositive, contradiction, and trivial and vacuous proofs, to name a few. Most of the content is already ready. We have a few technical challenges to overcome before it can be launched due to our new "proof" question format, but we have a clear idea of how these challenges are to be resolved, so 6-8 weeks is certainly realistic.
Hi, I'm Alex, Curriculum Director at Math Academy.
It is on our radar to allow students to "place out" of certain topics and modules if they feel ready. We'll call them "mini-diagnostics" or something similar when they're ready. I believe it will be worked on within the next few months.
Unfortunately, these things do take time to implement, but we are listening. FWIW, we're a tiny, bootstrapped company with literally two programmers (Justin, our ML/backend dev, and Jason, our founder and solo UX/UI) working on the entire codebase.
The content team is a little larger. We have around 12, mostly PhD mathematicians, working on the content, which is why the context is probably a little further ahead in some respects.
Hi, I'm Alex, curriculum director at Math Academy.
As Justin mentioned, there are several criteria that we must meet in our high-school pathway that aren't needed for studying higher-level (e.g., undergraduate) math, or they can be postponed. We decided to remove some of these in the Foundations series.
The idea behind the foundations series is to provide adult learners with the most efficient path possible to get onto the higher-level material.
Examples of topics that were removed from the high-school series to create the foundations series include some of the following:
* Various Geometry topics: All of the _essential_ geometry is covered. However, we removed topics on inscribed angles, Thales' Theorem, Triangle congruence, and similarity criteria (apart from the AA, which is the only one that seems to come up in practice), midpoint and triangle proportionality theorems, a fair amount of solid geometry, except what's fairly standard for calculus (volumes and surface areas of spheres, volumes of cones), lots of stuff on different types of quadrilaterals.
* Conic sections: The essentials are covered in both pathways. But in the high-school path, we go into a little more detail about foci, directrices, eccentricity, and utilizing their geometric definitions (e.g., focus-directrix properties).
* Trig identities and Equations: Covered in both pathways, but the high-school versions go into more detail and consider more cases.
* Some word problem/modeling topics.
* Other arbitrary Prealgebra topics: Divisibility rules, going into more detail about ratios in contextual settings, scientific notation, and some basic data representation topics that one would normally meet in Prealgebra.
* Slope fields. This will be covered in our upcoming differential equations course.
* Some analytical applications of differentiation that are quite specific to the BC Calculus exam: Identifying and removing point, jump, and infinite discontinuities and analyzing graphs of first and second derivatives.
* There are also fewer topics on related rates and optimization, though these topics are still covered.
* Some contextual applications of integration, like volumes of revolution and volumes of known cross-sections.
* Convergence tests for infinite series. When we get to that, these will be covered in real analysis, but other than infinite geometric series (which _is_ covered in Foundations), these tests don't show up too often anywhere else.
* Some ODE models, such as exponential and logistic growth and decay. We cover ODE basics in the foundations course, but particular models will be covered in the differential equations course.
* Taylor series. Again, this can be covered in the differential equations course for anyone wishing to take that course when it's ready.
Happy to answer any further questions you may have.
My colleague informs me that, contrary to my previous message, you get charged immediately, but you get an automatic refund if you cancel within 30 days.
Hi, I'm Alex, the curriculum director at Math Academy.
I can completely understand the skepticism and agree that many online courses are paper thin. That's where we're different.
For example, our BC Calculus course comprises 302 topics, each containing 3-4 knowledge points, so ~1060 knowledge points in total. Students must master each knowledge point to move on to the next. Our spaced repetition algorithms ensure that students are repeatedly tested on the material (we have quizzes every 150 XP or so). If they fail a question on a quiz or topic review, the system requires that they retake the failed topic. Students _cannot_ complete a course without mastering the entire thing.
Each knowledge point is connected to key prerequisites in the same course and lower courses. If a student stumbles on a particular knowledge point, our system can determine the most likely point of confusion and refer them to the associated key prerequisite topic (which they must pass to continue making progress).
We also have a couple of dozen multistep questions, similar to those you'd find on the BC exam (although the BC exam has about 4-5 parts per question, ours have about 9-10).
Regarding results, we had an 11-year-old sit the BC exam recently, and it looks like they will get a 5, the top mark. (For those that are unaware, students usually sit the BC Calc exam at the end of high school in the US, so 18). I admit that's an extreme case, but it's not isolated. I could reel off many success stories of students achieving real results on real tests after self-studying using our curriculum. We also have an associated school district program in Pasadena, California, where dozens of 8th-graders have achieved 4s and 5s in the BC exam, mostly learning using our system.
In terms of the required effort - provided you have no issues with the necessary prerequisite knowledge, you can get through our entire BC Calculus course by committing 40-50 minutes per day, five days per week, for around 5-6 months. Of course, if there are gaps in the prerequisite knowledge, then it'd take a little longer - but thankfully, our algorithms can detect missing knowledge and fill the gaps. That’s one of the advantages of having an intelligent, interconnected system comprising over 3000 topics!
As for our higher-level courses - some of these are still in development. However, our linear algebra course is comparable to several high-quality books on the subject (I like Lay, Anthony & Harvey, and Axler, though we use others). It currently has 176 topics, but many foundations are laid out in our Integrated Math III / Precalculus courses (vectors, matrices, basic determinants, inverse matrices, linear transformations in the plane), so the real number is around 200.
(click on the "content" tab to get a complete list of topics).
Could one of our students ace the GRE? That's a great question. We still need content on several key areas required for the GRE (e.g., Abstract Algebra, Real Analysis, Complex Analysis, and Graph Theory). These courses are still in development - we already have a lot of this content behind the scenes. That said, I'm confident that our students have the necessary tools to succeed in the parts of the GRE we currently cover. We don't "teach to the test," not even with BC Calc, but equipping our students with the necessary knowledge and skills to go from 4th grade math right the way up to acing the GRE (just as we've done with BC Calc) is one of our medium to long-term goals.
Happy to answer any further questions about the curriculum you may have.
Math Academy does not charge your card for the first 30 days. If you find it's not a good fit for then you can cancel within this period and you won't be charged. 30 days hopefully gives you enough time to determine whether it's a good fit or not.