Virginia DOE proposes math change up, stops advanced math in lower grades.

[lfromnj]

https://www.foxnews.com/us/virginia-accelerated-math-courses-equity

"[A]s currently planned, this initiative will eliminate ALL math acceleration prior to 11th grade," he said. "That is not an exaggeration, nor does there appear to be any discretion in how local districts implement this. All 6th graders will take Foundational Concepts 6. All 7th graders will take Foundational Concepts 7. All 10th graders will take Essential Concepts 10. Only in 11th and 12th grade is there any opportunity for choice in higher math courses."
He added that the concepts courses wouldn't eliminate algebraic ideas but rather interweave multiple strands of mathematics throughout the courses. Those included data analysis, mathematical modeling, functions and algebra, spatial reasoning and probability.

https://www.doe.virginia.gov/instruction/mathematics/vmpi/index.shtml

The Virginia Mathematics Pathways Initiative (VMPI) will:

Improve equity in mathematics learning opportunities
Empower students to be active participants in a quantitative world
Encourage students to see themselves as knowers and doers of mathematics
Identify K-12 mathematics pathways that support future success
Collaborate with multiple stakeholder to advance mathematics education
The VMPI will develop an initial vision for mathematics education in K-12 that will require feedback from many different stakeholders across the Commonwealth.  This feedback will be critical when the Mathematics Standards of Learning revisions in 2023 reflect the goals and recommendations of this Initiative. Possible piloting of high school level mathematics courses prior to full implementation is now being considered. This Initiative will establish an innovative direction for mathematics education in Virginia that will benefit all students.

Not 100% sure on the full veracity of this and I don't like the idea of sticking kids who really struggle with math in the same class as kids who are good with math once past elementary school. So completely eliminating the option for smarter kids to go ahead would be a really bad idea and seems like wokism out of control for the sake of "equity".

However on the other hand, I do like the idea of these integrated courses which weaves the subjects together for the lower grades, and then the focus on more specialized math courses.


https://www.doe.virginia.gov/instruction/mathematics/vmpi/infographic-vmpi-virginia.pdf



They are absolutely correct in that calculus is not for everyone and end tier math courses should be more diversified. Love the idea of other courses being considered advanced math as calculus is a relatively useless subject for most of the country going to college.


Overall seems like a very good base concept but unfortunately the "woke "part of this could seriously hurt it.


They do claim they will still provide differentiated education but that part may need to be fleshed out better.

Pyle added that VMPI "aims to support increased differentiated learning opportunities within a heterogeneous learning environment, that will promote greater access to advanced mathematical learning for all students before high school graduation.

The heterogenous part is what worries me. Its a bit of "wokespeak" and  I think they do intend to remove advanced courses in earlier grades by judging what heterogenous means.

I know its just one state and its not even finalized yet but It feels like an interesting debate. I would be excited to see this idea move forward with some changes.

[GeneralMacArthur]

I disapprove.  For many different practical fields such as probability and statistics or analysis/modeling, there's a basic understanding you can gain, and then a more advanced understanding that only comes from having a solid foundation in calculus and other intermediate math concepts.  If you're really good at math, you should be focused on building that solid foundation as quickly as possible.  Learning the practical stuff early is kind of pointless because you're not going to use it yet, so you're just going to have to learn it again later.

That said I don't think an extra course on "practical math" in the middle of high school would hurt.  Especially teaching people how to think about probability/statistics, that's a fundamental skill that most Americans are missing.  But it shouldn't come at the expense of advancing in algebra/trig/calculus as fast as possible.

[Sestak]

Mixed feelings about the laning. I've seen math laning be manipulated and abused through persistent parent lobbying, but I don't think that's what's happening here and so am not sure about it. I'm not even really worried about the speed of the material - so long as someone proficitent can still skip ahead in math. The main concern with non laning is that you lose the chance to be met with a higher standard of rigor, which is key for an understanding that you can not just use but also build off of with later learning.

I'm with MacArthur (surprisingly) on at least some of the advanced non-calculus stuff. Not all of it, but, for instance, I'm struggling to think of what "Mathematical Modeling" is even going to be without calculus techniques?

Also as a pure math person I naturally have to disapprove of the idea of replacing math almost entirely with applied math or subjects that aren't even math (such as CS or stats). Ironically, the two CS 1/2 credit options seem like the most interesting courses to take on that 11-12 grade list.

So, in all, a very mixed bag but a lot I'm skeptical of. If they do go ahead with it it'll be insightful to see how it goes, I guess.

[DaleCooper]

This seems like a bad idea. For elementary school it probably won't matter much, but there should definitely be advanced math classes available starting in around 6th grade. Classes are split this way for the benefit of all of the students and it has nothing to do with leaving anyone behind or privileging certain students. In fact, placing struggling students in classes that require them to learn faster than they're capable of will probably hurt them even more than it hurts the advanced students to be placed in the more basic classes. It isn't even a question of intelligence so much as aptitude with a certain subject since I imagine it's not too uncommon for a student to be in a standard math class while being in an advanced English class or vice versa.

[lfromnj]

I disapprove.  For many different practical fields such as probability and statistics or analysis/modeling, there's a basic understanding you can gain, and then a more advanced understanding that only comes from having a solid foundation in calculus and other intermediate math concepts.  If you're really good at math, you should be focused on building that solid foundation as quickly as possible.  Learning the practical stuff early is kind of pointless because you're not going to use it yet, so you're just going to have to learn it again later.

That said I don't think an extra course on "practical math" in the middle of high school would hurt.  Especially teaching people how to think about probability/statistics, that's a fundamental skill that most Americans are missing.  But it shouldn't come at the expense of advancing in algebra/trig/calculus as fast as possible.

They do say prereq knowledge may be necessary so your concern is valid although I would calm down a degree.

This seems like a bad idea. For elementary school it probably won't matter much, but there should definitely be advanced math classes available starting in around 6th grade. Classes are split this way for the benefit of all of the students and it has nothing to do with leaving anyone behind or privileging certain students. In fact, placing struggling students in classes that require them to learn faster than they're capable of will probably hurt them even more than it hurts the advanced students to be placed in the more basic classes. It isn't even a question of intelligence so much as aptitude with a certain subject since I imagine it's not too uncommon for a student to be in a standard math class while being in an advanced English class or vice versa.

This part of the proposal is definitely a bad idea IMO but the whole proposal isn't. It is obviously unfair to teachers to expect them to cater to the needs of those far behind in math but also those doing very well , all in one classroom.

[DaleCooper]

This seems like a bad idea. For elementary school it probably won't matter much, but there should definitely be advanced math classes available starting in around 6th grade. Classes are split this way for the benefit of all of the students and it has nothing to do with leaving anyone behind or privileging certain students. In fact, placing struggling students in classes that require them to learn faster than they're capable of will probably hurt them even more than it hurts the advanced students to be placed in the more basic classes. It isn't even a question of intelligence so much as aptitude with a certain subject since I imagine it's not too uncommon for a student to be in a standard math class while being in an advanced English class or vice versa.

This part of the proposal is definitely a bad idea IMO but the whole proposal isn't. It is obviously unfair to teachers to expect them to cater to the needs of those far behind in math but also those doing very well , all in one classroom.

Yeah, I like their plans for integrated courses for elementary level students. I also think it's great that they're emphasizing that there are multiple paths toward a successful career after high school rather than just a universal focus on college prep or nothing at all, but that's why it seems odd and out of place for them to also try a one size fits all approach to math courses.

[SInNYC]

I hate this with a passion. There seems to be this national belief, both at the school and college level, that math is obsolete and we should be teaching "coding" and "statistics" instead. Its mostly promulgated by those educators who were bad at math.

But the coders end up teaching how to download code and change "hello world" to "hello america" - ask any software house how hard it is to find a programmer who can do more than that. And the statistics people teach how to run a program that runs T tests, with no clue about what it actually means other than as a list of scenarios where you run T tests (hint: you need algebra to figure out how to go from distributions to hypothesis testing).

The single most important thing we can do to improve coding and stats skills is to teach algebra more rigorously. By this, I mean using algebra to model problems (eg word problems), instead of just as a technique to solve for x.

[John Dule]

In the woke future, being exceptional is oppressive.

[Benjamin Frank]

I disapprove.  For many different practical fields such as probability and statistics or analysis/modeling, there's a basic understanding you can gain, and then a more advanced understanding that only comes from having a solid foundation in calculus and other intermediate math concepts.  If you're really good at math, you should be focused on building that solid foundation as quickly as possible.  Learning the practical stuff early is kind of pointless because you're not going to use it yet, so you're just going to have to learn it again later.

That said I don't think an extra course on "practical math" in the middle of high school would hurt.  Especially teaching people how to think about probability/statistics, that's a fundamental skill that most Americans are missing.  But it shouldn't come at the expense of advancing in algebra/trig/calculus as fast as possible.

Totally disagree.  Calculus is very useful if you complete at least first level differential calculus and can pass ( ) first level integral calculus.  However, most high school math ends with pre calculus (AKA algebra II) which by itself is entirely abstract and meaningless.  Multiple studies show that algebra II turns many high school students off of mathematics to the point where they fail to graduate and can't attend any post secondary institution as a result.

Also, for those students who do pass Algebra II in high school (which is the majority to be sure) most of them, if they go on to college are not going to take calculus in college.  So, again, teaching algebra II by itself is still a waste of time in high school.  

So, teaching algebra II by itself is a bad thing.

At the end of the day, all the curriculum makers have in favor of teaching algebra II in high school are snobbish arguments about the supposed wonders of teaching students meaningless abstractions.

As to teaching 'practical math', probability and statistics.  It is, I gather, correct, that a full understanding of probability and statistics does require calculus, however, it is completly false to argue that there is no benefit to critical thinking skills from teaching one or two probability and statistics courses that do not require any knowledge of calculus.

So, ultimately there is something of a choice: either teach probability and statistics in high school or teach advanced mathematics to the level that first level differential and integral calculus are taught as well (students in high school physics classes would be very happy with that, I'm sure.)  

I don't necessarily have a preference one way or the other, but as somebody else here mentioned, the quality of the mathematics teaching in high school tends not to be great and calculus teaching tends to require better teaching than teaching probability and statistics.  Contrary to some of the arguments, since it's actually impossible to magically conjure up thousands of better high school math teachers, I argue teach probability and statistics in high school, and leave algebra II for those who take calculus in college.

Of course, if high school students want to take algebra II as an elective, that's wonderful.

[Benjamin Frank]

Improve equity in mathematics learning opportunities
Empower students to be active participants in a quantitative world
Encourage students to see themselves as knowers and doers of mathematics
Identify K-12 mathematics pathways that support future success
Collaborate with multiple stakeholder to advance mathematics education

As I posted above, I largely agree with these goals (I don't agree with doing away with advanced class math electives) but the number of buzzwords/phrases used here is cringeworthy.

1.equity
2.learning opportunities
3.empower
4.active participants
5.quantitative world
6.knowers and doers
7.pathways
8.collaborate
9.stakeholder

Leaving out articles and prepositions, I counted 33 words in that explanation, meaning around 1/3 of the total words used are obnoxious buzzwords/phrases.

Well, I'm off right now to facilitate participation with a stakeholder I need to touch base with.

[JA]

How does it benefit anyone to withhold advanced mathematics from students capable of learning it successfully and forcing them to share in the same lessons as children who struggle at math? Terrible idea.

I was in advanced classes, then they said there wasn’t enough space available in 4th and 5th grade for me; I was part of the unlucky who lost that lottery at my elementary school. I became bored of school, my grades declined, and they never truly recovered until my senior year. I’d hate to see other advanced students face that same fate. Fortunately for me, I was still invested in learning for learning’s sale and chose to educate myself on a variety of subjects that were never addressed in school; however, I do believe I would’ve benefitted more from advanced classroom education - and so would most students.

[Benjamin Frank]

How does it benefit anyone to withhold advanced mathematics from students capable of learning it successfully and forcing them to share in the same lessons as children who struggle at math? Terrible idea.

I was in advanced classes, then they said there wasn’t enough space available in 4th and 5th grade for me; I was part of the unlucky who lost that lottery at my elementary school. I became bored of school, my grades declined, and they never truly recovered until my senior year. I’d hate to see other advanced students face that same fate. Fortunately for me, I was still invested in learning for learning’s sale and chose to educate myself on a variety of subjects that were never addressed in school; however, I do believe I would’ve benefitted more from advanced classroom education - and so would most students.

This is why there need to be charter schools that can set their own curriculum (with minimum requirements of course.)

[JA]

How does it benefit anyone to withhold advanced mathematics from students capable of learning it successfully and forcing them to share in the same lessons as children who struggle at math? Terrible idea.

I was in advanced classes, then they said there wasn’t enough space available in 4th and 5th grade for me; I was part of the unlucky who lost that lottery at my elementary school. I became bored of school, my grades declined, and they never truly recovered until my senior year. I’d hate to see other advanced students face that same fate. Fortunately for me, I was still invested in learning for learning’s sale and chose to educate myself on a variety of subjects that were never addressed in school; however, I do believe I would’ve benefitted more from advanced classroom education - and so would most students.

This is why there need to be charter schools that can set their own curriculum (with minimum requirements of course.)

Public education is solely concerned with creating a workforce of uniform laborers and managers capable of performing just well enough on standardized tests to ensure the continued existence of our economy. They really aren’t interested in cultivating young minds truly invested in learning. Parents need to play a larger role in their child’s education, but that requires time and resources that they either don’t have or won’t invest. Imagine how many brilliant minds are lost due simply to daily traumatic stress in their lives. What do we do about neglectful parents? Traumatic neighborhoods? So many factors are involved in the failure of our nation’s educational system, I don’t know where we truly begin to address it.

[Associate Justice PiT]

     Advanced tracks for gifted students are critical, and we hurt them a lot by denying them those opportunities. Otherwise the concept of tracking has merit, but is at odds with the nature of university education which focuses in many departments on training students for academia and expecting them to manage the transition to industry if they choose to go that route.

     If we are going to re-envision math education, it needs to occur as part of a comprehensive system that encompasses both K-12 and higher education. Just tackling one and not the other does not have much point and will cause more problems than it solves. Obviously this would be a project beyond the scope of the Virginia DoE, and likely will never be implemented in any actual sense for that reason.

[Alcibiades]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

[Former President tack50]

Wow the state of Virginia is mega based. Virginia may be for lovers, but I sure do love the Virginia DOE

That seems like a great reform to me. To be honest it reminds me of the very own way I got taught math; where every student got the same curriculum up to year 9. Year 10 math got divided into Math "A" (mostly statistics, intended for future humanities students) and Math "B" (functions, equations and what not, intended for future STEM, sciences and medical students)

Year 11 and 12 also had math packaged in the same way ("Applied Math" vs "(pure) Math"), except you could drop math alltogether if you chose the "arts" path (very rare since very few schools offer it) or the "pure humanities" path (more common). If you chose the social sciences path you got "applied math" and if you chose one of the STEM paths you had plain old "Mathematics".

No laning or splitting math into Calculus/Algebra/Geometry/Trigonometry/etc, which feels very unnecessary to me

Also I am suprised that most of the red avatars and left leaning people so far have come out against the proposal claiming it harms gifted kids and what not while the only one I've seen in favour is noted libertarian lfromnj

[Alcibiades]

Wow the state of Virginia is mega based. Virginia may be for lovers, but I sure do love the Virginia DOE

That seems like a great reform to me. To be honest it reminds me of the very own way I got taught math; where every student got the same curriculum up to year 9. Year 10 math got divided into Math "A" (mostly statistics, intended for future humanities students) and Math "B" (functions, equations and what not, intended for future STEM, sciences and medical students)

Year 11 and 12 also had math packaged in the same way ("Applied Math" vs "(pure) Math"), except you could drop math alltogether if you chose the "arts" path (very rare since very few schools offer it) or the "pure humanities" path (more common). If you chose the social sciences path you got "applied math" and if you chose one of the STEM paths you had plain old "Mathematics".

No laning or splitting math into Calculus/Algebra/Geometry/Trigonometry/etc, which feels very unnecessary to me

Also I am suprised that most of the red avatars and left leaning people so far have come out against the proposal claiming it harms gifted kids and what not while the only one I've seen in favour is noted libertarian lfromnj

Yeah, from what I understand of US maths education, the splits seem quite odd, and there seems to be excessive focus on calculus. Pure vs applied is also the division here (although you don’t get a choice - you have to do both if you continue with maths beyond 16).

[lfromnj]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.  Also even then the focus on calculus for more advanced students is a bit excessive IMO.

[lfromnj]

Wow the state of Virginia is mega based. Virginia may be for lovers, but I sure do love the Virginia DOE

That seems like a great reform to me. To be honest it reminds me of the very own way I got taught math; where every student got the same curriculum up to year 9. Year 10 math got divided into Math "A" (mostly statistics, intended for future humanities students) and Math "B" (functions, equations and what not, intended for future STEM, sciences and medical students)

Year 11 and 12 also had math packaged in the same way ("Applied Math" vs "(pure) Math"), except you could drop math alltogether if you chose the "arts" path (very rare since very few schools offer it) or the "pure humanities" path (more common). If you chose the social sciences path you got "applied math" and if you chose one of the STEM paths you had plain old "Mathematics".

No laning or splitting math into Calculus/Algebra/Geometry/Trigonometry/etc, which feels very unnecessary to me

Also I am suprised that most of the red avatars and left leaning people so far have come out against the proposal claiming it harms gifted kids and what not while the only one I've seen in favour is noted libertarian lfromnj

Well I still oppose the proposal as it stands because of the stopping of the accelerated courses. It was also a pain to read through the woke buzzwords like Frank noted. However I think some of the idea would make some sense IMO.

[Benjamin Frank]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.

1.My understanding is that Algebra II and Pre Calculus are the same thing.  Pre Calculus is what Algebra II is called in college for those who want/need to take remedial math courses.

Edit to Add: the previous poster was correct.  Pre Calculus is in grade 12, but it is an extension of Algebra II.

2.Algebra II is the third math course in high school and will guide you through among other things linear equations, inequalities, graphs, matrices, polynomials and radical expressions, quadratic equations, functions, exponential and logarithmic expressions, sequences and series, probability and trigonometry.

Pre calculus in high school ends off with students able to answer the 'fundamental theorem  of calculus.' So, all of the hard work with meaningless abstract math, but none of the payoff.

3.What the previous commenter referred to as 'mechanics' is part of physics classes.

[ingemann]

To be honest I don’t think it make any real difference, I didn’t get grades before seventh grade and we didn’t have classes for student on a more advanced level than the us other, and I must admit that Americans don’t really seem better at math. In general if the teacher can keep order in the class the children will suck up knowledge. Of course if you have dysfunctional schools with teachers being unable to enforce order, I can see why pulling the well functioning students away into separate classes would be a good idea.

[Alcibiades]

I think the unique challenge with maths curricula in secondary education (in general; I’m not that familiar with the US*, but this applies everywhere) is the wide variety of uses pupils go onto have for maths. For most, it will just be being functionally numerate. But for the more able, they will actually go onto use it in their university studies - and within this group, you further have a spectrum from those who need it for maths itself or physics, to somewhat less mathematical natural sciences like biology and chemistry, to the social sciences. For this reason, I do think it really makes sense to stream maths curricula from the age of 13 or 14.

*Could someone clarify for me what students in their final two years of high school typically learn in the US in maths? In the UK, for those who choose maths (students at this age in generally have a free choice of any three or four subjects - you can also choose further maths, in addition to normal maths (as I did), the only subject for which this is possible, so that maths takes up half your timetable), it’s a range of pure maths (functions, trig, calculus, logarithms, proof, vectors, series, binomial expansion) and statistics (hypothesis testing, conditional probability) and mechanics (constant and variable acceleration, forces on an object, moments, projectiles). Further maths extends these topics and introduces ones such as complex numbers, matrices and differential equations.

Generally the most base standard track would develop all the principles till 7th grade and starts Pre-Algebra in 8th. Algebra in 9. Geometry in 10 . Algebra 2 in 11 and Pre Calc in 12. The Algebra > Geometry> Algebra 2 gap is a pretty big deal IMO and really should not be done. Accelerated paths also exist and for example one would start Pre Algebra in 7th or 8th and then be doing Calc in 11th or 12th.

What (briefly) is the contents of these courses? So do you spend the whole of 10th grade doing geometry and not touching other (more relevant, IMO, or maybe that’s just because I never particularly liked geometry compared to algebra ) areas of maths?

[○∙◄☻¥tπ[╪AV┼cVê└]

Math was boring enough without some rules like this.

[Malarkey Decider]

God this is so stupid. It just limits the potential of those who wish to get ahead and due as much work as possible. Because of the way my High School is set up, I'm in Pre-calc and AP Stats this year. If this stupid system was set up in Georgia, I would be forced to cater to the capabilities to those who did not want to do that.

[Sestak]

The geometry split of algebra is a tough nut to crack. On the one hand, geometry, if taught properly, is extremely useful for teaching rigorous proof and reasoning skills as opposed to simply rote computation; thus it or an adequate replacement should be part of any reasonable path.

On the other hand, splitting algebra in two like that is very awkward indeed and puts a lot of people in a strange place before heading into Alg II.