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Jann in TX

Musings about the Common Core and high school Math (longish)

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Please do not make this a debate about how the Common Core is to be implemented (and the infringement of personal rights/state's rights) or the tracking of students...

Since I've been ill for the past 2 weeks (and thus homebound) I decided to do more reading/research and speculate how the Common Core will change the scope of 'traditional' high school math in the US.

In the US we have had an 'unspoken' set of standards in place--driven by state textbook committees and the purchasing of textbooks that meet the 'state goals'.  Because of this most high school Algebra 1 texts contain virtually the same teaching concepts.  The same goes for Algebra 2.  Geometry has a slightly higher variance--outside of formula work.

 

The US progression has been lacking (compared to the ‘rest of the world’) in a few key conceptual areas that only a few of our advanced students have studied-- namely number theory, probability and statistics.  A good percent of our middle school students have had an introduction to these concepts--but they are not true/pure Algebra or Geometry so they are not part of traditional high school textbooks for those subjects.  The US progression has also been lacking in critical thinking and application-- this is one of the biggest changes the Common Core is trying to make (not necessarily a bad thing).

 

After reading through the Common Core standards a few times I am finding that I am not disagreeing with them-- I’m more curious about what would be the BEST way to align our curriculum to these standards in the short time allowed (knowing that it takes YEARS to develop solid curriculum).

 

The biggest change I see is in 6th-8th grade math.  Much of a ‘traditional’ Algebra 1 course is now being moved to the middle grades.  The Common Core standards for grades 1-7 supposedly ‘prepare’ students for Algebra 1 in 8th grade with states having the option of students taking Algebra 1 in 9th grade.  It sounds fine-- nothing seems out of ordinary until you look at the standards and see that a great portion of a traditional Algebra 1 course is now taught in grades 6-8 with the Common Core 8th grade math being quite Algebra heavy.   The Common core allows for the traditional sequence of ‘Algebra 1,  Geometry and Algebra 2’ but those courses will only exist in name as the content will have to shift to include the new standards.

 

Basically, the Algebra 1, Geometry, Algebra 2 traditional courses will now need to include probability, statistics and trigonometry (outside of right triangle Trig that is part of most current Geometry or Algebra 2 texts). So we now have 4 years of traditional US math crammed into 3... unless you count 8th grade math as the 4th year...  

 

The Common Core does allow for more advanced or ‘college prep’ Algebra at the high school level.  Students can take a Math 4 (similar to Pre-Calc/advanced Statistics) their Sr year.  Some states may opt for Math 1 to be taken in 8th grade (the current models have provisions for Math 6 and 7 to be combined into one year).  This would allow for Calculus to be taken in high school.  The Common Core does not dictate standards for Math 4 or Calculus-- as these are still seen as college-level courses.

 

I predict an increase in ‘integrated math texts’ at the high school level-- as a few states have already moved to.  8th grade math will be the new foundation (instead of Algebra 1) and Math 1, 2 and 3 will be the high school standards.

 
I’m not in disagreement with these standards and the need for change-- I’m wondering HOW and WHEN to begin this transition.

My concern is with my current 8th grade and 9th grade students in Algebra 1.  The changes in the college entrance tests WILL affect them... how do I (we) prepare these students when the curriculum has not been developed yet and the standards do not provide a clear list of necessary concepts (just a general scope)?

 

Homeschoolers (and schools in the states that have not signed on to the Common Core) are not ‘bound’ to teach to the Common Core-- however the inevitable is happening as within a few years the standard college entrance tests (PSAT/SAT and ACT) will be based on the Common Core.  The depth of change in the tests is yet to be seen-- but homeschoolers WILL be affected.

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I have wondered about this. I agree that the standards themselves seem like a reasonable solid math progression (though I am afraid the progression will be out of the reach of some students) but implementation during the transition period is problematic. Have you looked at how the common core standards compare with the integrated programs that are out there? I'm thinking of the secondary Singapore programs, for example.

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My son's school uses the Common Core aligned Larson Algebra I book.  I found it striking how much of what I assumed to be part of a standard Algebra I course was left out.  Specifically, the following topics did not appear anywhere in the text:

 

Algebraic fractions and fractional equations

Square roots (except for how to press the square root key on the calculator)

Dividing polynomials

 

There were other more minor topics that were not addressed as well.  (To its credit, the CC aligned Larson Algebra II text does not spend much time on review, so they do get some time back that way.)

 

Because fractions and square roots were left out, when they got to the quadratic formula, they were unprepared to really understand how it was derived.  Also, the book instructed them to give answers in decimal form when leaving them in square root form would have been preferable.  To my son's teacher's credit, she had them leave the answers in square root form, but did not specifically teach how to simplify them, which I found annoying, so I taught him myself.

 

 

 

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I have wondered about this. I agree that the standards themselves seem like a reasonable solid math progression (though I am afraid the progression will be out of the reach of some students) but implementation during the transition period is problematic. Have you looked at how the common core standards compare with the integrated programs that are out there? I'm thinking of the secondary Singapore programs, for example.

 

The problems with jumping to an integrated program such as Singapore at the high school level (Algebra 1 or Math 1) is that unless the student has used that type of program before they will be at a loss (not have the background concepts and models mastered).  These integrated programs are built on previous levels.

 

Something else to ponder-- is that the US's lack of emphasis on critical thinking and problem solving in the elementary/middle school years has made our current students 'soft'-- a great majority are lacking these skills that they will now suddenly be expected to have mastered...

 

Also the demands of the additional concepts will force the 'overlap' currently seen in US high school curriculum to vanish.  A great majority of my current students have benefitted from this overlap (as MENTAL MATURITY happens at different rates for different students).  We are expecting some students to run before they have a chance to learn to walk. 

 

On the up side I do see the upper 10-20% of students rising to the challenge-- they will go farther (mathmatically) than they would have under the current system.  I also see a larger number of studnets lagging seriously behind....

 

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I agree that the new standards, as you've presented them as I haven't read them in detail myself, sound like a good change.  I think it's ironic that Saxon recently came out with their separate algebra and geometry texts.  It sounds like the 3rd edition integrated texts would fit the new standards nicely.  Probability is incorporated as are some other topics not normally included.  I have no idea if they contain all of the "new" content or not.  I know Saxon doesn't work for all students, but I wouldn't be surprised if schools are giving it a look.   Wonder if they'll soon come out with 5th editions which would basically be the 3rd editions repeated with more critical thinking and whatever areas aren't already included.

 

I hope you're feeling better soon Jann.   Interesting topic and I think you're smart to be thinking ahead.

 

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My son's school uses the Common Core aligned Larson Algebra I book.  I found it striking how much of what I assumed to be part of a standard Algebra I course was left out.  Specifically, the following topics did not appear anywhere in the text:

 

Algebraic fractions and fractional equations

Square roots (except for how to press the square root key on the calculator)

Dividing polynomials

 

Would not square roots be a pre-algebra topic?

And is not polynomial division typically covered in algebra 2?

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My son's school uses the Common Core aligned Larson Algebra I book.  I found it striking how much of what I assumed to be part of a standard Algebra I course was left out.  Specifically, the following topics did not appear anywhere in the text:

 

Algebraic fractions and fractional equations

Square roots (except for how to press the square root key on the calculator)

Dividing polynomials

 

 

The Common Core has square roots and exponents (even negative exponents) taught at the Math 8 level.

 

I introduce dividing polynomials in Algebra 1 (but very few students actually 'get it' until Algebra 2 when more time is spent on the process).

 

The Common Core does not dictate what topics in the high school progression are to be covered at any given level-- just that they are all to be covered over a 3 year period (Math 1, 2 and 3) or basic 9th, 10th and 11th grades (with option to begin sequence a year earlier for high achievers).  This lack of defined structure makes me wonder what the 'new' versions of the college entrance tests will be based on...

 

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Aren't square & cube roots typically part of pre-algebra rather than algebra 1? I know that was one concern I had when looking at what to do after Singapore Primary Mathematics. I ended up deciding to continue on with Singapore Discovering Mathematics 7 (which does cover roots) and supplement that with Horizons Pre-Algebra (which also covers roots).

 

I've got an older edition of Larson's Elementary Algebra so I'll have to check whether it covers roots.

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My concern is with my current 8th grade and 9th grade students in Algebra 1.  The changes in the college entrance tests WILL affect them... how do I (we) prepare these students when the curriculum has not been developed yet and the standards do not provide a clear list of necessary concepts (just a general scope)?

 

I find that a student who has a strong conceptual foundation in arithmetic and algebra 1, with emphasis on critical thinking and problem solving, will quickly pick up new topics at test prep. We noticed that when DD studied for the SATII; there were topics we had never covered, but since her overall math base is strong, adding a few new topics at test prep was really no big deal.

If they just say " some probability and number theory" will be included, without specifying topics, I would think a student who has been taught to approach math on a conceptual, rather than procedural, level, should have no difficulties grasping those comparatively easy concepts.

So, maybe the best preparation when no detailed info is available, might be creating a strong foundation in critical thinking and problem solving - and then filling in a few gaps when the new tests are revealed. That is the approach I am taking with my current 9th grader (and have been taking since middle school)

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Would not square roots be a pre-algebra topic?

And is not polynomial division typically covered in algebra 2?

 

In the typical US math progression square roots are only introduced in Pre-Algebra on the level such as 'the square root of 25 is 5'.  Most Pre-Algebra curriculums only touch on them and very few teach how to simplify radicals (usually found in traditional Algebra 1 texts).  There seems to be a trend to 'get to Algebra 1 as quickly as possible' so most meatier Pre-Algebra texts are infrequently used or that level is skipped.

 

Current US Algebra 1 students have little application for polynomial division (not to be confused with simplification of monomials).  It is 'standard' for the Algebra 1 texts to have an introduction to polynomial division-- but the 'real' coverage is at the Algebra 2 (Intermediate Algebra) level.  Most Common Core texts are removing the 'overlap' (mainly the introduction) of such concepts.

 

 

MOST US curriculum (especially the ones popular with the homeschooling community) is very weak on critical thinking and modeling.

The Common Core standards have more than just a mere introduction to number theory/probility/statistics-- more like the inclusion of a full credit course (combination of these 3) much much more advanced than what is taught at the current middle school level.

 

I know (from your past posting history) that you have used a strong mathmatical progression with your students-- AOPS and similar programs that develop the skills that the Common Core is trying to foster. 

 

MOST current US middle school and high school students are not receiving the same level of foundation so they will need more than just a simple test prep book to catch up.

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So I pulled out the 3 algebra 1 texts I have on my shelf: Larson's Elementary Algebra 4th ed., CGP California Algebra 1 (unknown edition, 2007 copyright date), and Prentice-Hall Experiencing Introductory Algebra by Thomasson & Pesut (unknown edition, 1999 copyright).

 

Larson has an entire chapter on roots & radicals. The CGP has a 5 page section in the 1st chapter (which appears to be a quick review of pre-algebra) on basic roots and then a 4 page section in chapter 7 on solving quadratic equations involving roots. The Thomasson & Pesut has a 12 page section in chapter 10 on solving quadratic equations involving roots.

 

So in 2 of the 3 books, roots only get touched upon briefly.

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As to why I have 3 algebra 1 books in addition to Singapore DM 8 on my shelf, I like the "real world" word problems found in the Larson and Thomasson & Pseut books. My DD is a generally strong math student and can solve straightforward equations easy-peasy. However, she has always struggled with word problems and that's the form that IRL math takes. So I want to make sure that she gets plenty of practice with solving word problems.

 

The CGP I got in case our virtual charter needed to see some work done out of a CA-approved algebra 1 book. With the move to Common Core, I think it probably won't be necessary but I'm not returning the book to the lending library until I have confirmation.

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So I pulled out the 3 algebra 1 texts I have on my shelf: Larson's Elementary Algebra 4th ed., CGP California Algebra 1 (unknown edition, 2007 copyright date), and Prentice-Hall Experiencing Introductory Algebra by Thomasson & Pesut (unknown edition, 1999 copyright).

 

Larson has an entire chapter on roots & radicals. The CGP has a 5 page section in the 1st chapter (which appears to be a quick review of pre-algebra) on basic roots and then a 4 page section in chapter 7 on solving quadratic equations involving roots. The Thomasson & Pesut has a 12 page section in chapter 10 on solving quadratic equations involving roots.

 

So in 2 of the 3 books, roots only get touched upon briefly.

 

Exponents and roots will now be a stronger part of Math 8:

 

CCSS.Math.Content.8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 Ã— 3–5 = 3–3 = 1/33 = 1/27.

 

Very few traditional US Algebra 1 texts teach negative exponents--and typically as an introductory level to be expanded in Algebra 2.. but  now the students will need to have mastered this concept in Math 8 before moving into Math 1 (9th grade and traditionally Algebra 1).

 

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... I think it's ironic that Saxon recently came out with their separate algebra and geometry texts.  It sounds like the 3rd edition integrated texts would fit the new standards nicely.  Probability is incorporated as are some other topics not normally included.  I have no idea if they contain all of the "new" content or not.  I know Saxon doesn't work for all students, but I wouldn't be surprised if schools are giving it a look.   Wonder if they'll soon come out with 5th editions which would basically be the 3rd editions repeated with more critical thinking and whatever areas aren't already included.

 

Saxon will be coming out with a new edition that is Common Core compliant ( they will have to add additional topics).  I see them going back to the full integration and doing away with the separate Geometry.

 

I know (internationally speaking) that there are other curriculm providers that have integrated materials that are not taught using the 'Saxon method'... we just do not have many US choices at the current time--give it 5-10 years and there will be MANY to choose from.  Most publishers are rushing to create Common Core supplements and are rearranging their chapters buying time until they can rework the progression.

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FWIW, while AoPS Prealgebra is much deeper than standard texts, simplifying square roots of non-square integers is definitely covered there, as well as negative exponents.  I thought there was some in Dolciani but I can't remember and I'm not home today to look.  I don't think simplifying square roots is terribly difficult to teach (I have found myself making up silly language, "unsquaring," to describe the process of taking out the perfect square factors from under the radical) though resources for younger grade levels may be harder to find.  There are a few AoPS Prealgebra videos that may be useful for anyone on this topic.  I wouldn't be surprised if MM7 teaches simplifying - though there are only two lessons on square roots that I see in the old proposed TOC for 7, it is supposed to be both a prealgebra and CC-aligned.

 

I'm a little confused on the extent to which integration in the high school levels will really be necessary, but I'll have to read about it later...

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Would not square roots be a pre-algebra topic?

And is not polynomial division typically covered in algebra 2?

 

I never thought of simplifying something like the square root of 50x^3y^7 as a prealgebra topic, but I could be wrong.  I know that it was not assumed knowledge in the CC aligned Larson Algebra I text.  It is in the CC aligned Larson Algebra II text.

 

Polynomial division is covered in Jacobs, but perhaps it is more often found in Algebra II texts.

 

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I'm hoping this shift will eliminate my struggle over what to officially call my DCs math courses as we are really liking Singapore's integrated program. My oldest is in their new CC correlated 7A. We like the presentation and the application problems. Looking ahead, 7B (which we'll begin at the end of January) covers mostly geometry problems. It certainly seems advanced for 7th grade math, but since we have been following the SM sequence (with LoF) it's a good fit for us.

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NY has had integrated math for a few years now. As always, the antiintellectual districts do not teach all the Regent's objectives. Students are likely to find that units are omitted in order to spend more time on basics, so that more students will earn a 65 and pass. Families here hire a tutorfor the missing units, to score in the 90s, especially for nonaccelerated students interested in math and science college degrees.

 

Back in the Jurasssic, my district used the entire Dolciani texts, one per school year.These texts have probability integrated. It was not a problem for the top 25% of students to do that much.

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The Common Core has square roots and exponents (even negative exponents) taught at the Math 8 level.

 

I introduce dividing polynomials in Algebra 1 (but very few students actually 'get it' until Algebra 2 when more time is spent on the process).

 

The Common Core does not dictate what topics in the high school progression are to be covered at any given level-- just that they are all to be covered over a 3 year period (Math 1, 2 and 3) or basic 9th, 10th and 11th grades (with option to begin sequence a year earlier for high achievers).  This lack of defined structure makes me wonder what the 'new' versions of the college entrance tests will be based on...

 

 

Jann, thank you for taking the time to walk through the basics of math under the Common Core. I need to read more explanations like that as I tend to still have knee-jerk reactions to many aspects of CC.

 

If you could, would you please elaborate on the part in bold and the possible implications? My older kids were part of our district's move to a new math program. I can't for the life of me remember which one it was, but I do remember that instead of a traditional text the topics were divided out into separate books. My dd was in green hall and she started 7th grade year with "Fractions" while the neighbor kid in blue hall started with "Probability," and the other neighbor kid in orange hall started with "Decimals." I don't know that those were the specific titles, but you get the idea. I always wondered what happened if kids changed schools. The program was disastrous here for many reasons, but the primary one was that the transition period was very poorly planned. Many students were left with huge holes in their skill sets.

 

If there is no set progression as to when topics are covered, wouldn't this create more problems for teachers? Jann, I'm sorry for being so dense.

 

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So far, I have not heard anything mentioned not covered somewhere in A Beka. (I think we are the only family on this board that uses A Beka math all the way through.). But, I cannot remember what years each topic was covered. I really hope common core will not make much difference in our homeschool as I am getting old and tired with only 2 1/2 years left to go. Has anyone familiar with A Beka done an analysis?

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Exponents and roots will now be a stronger part of Math 8:

 

CCSS.Math.Content.8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 Ã— 3–5 = 3–3 = 1/33 = 1/27.

 

Very few traditional US Algebra 1 texts teach negative exponents--and typically as an introductory level to be expanded in Algebra 2.. but  now the students will need to have mastered this concept in Math 8 before moving into Math 1 (9th grade and traditionally Algebra 1).

 

 

This entire conversation is out of my league.   I just wanted to share in reference to the bolded that Foerster alg 1 had an entire chapter dedicated to exponents, including negative exponents.   Just sharing in case others reading this thread feel like they are going to need to abandon all non-CC textbooks.   Foerster is definitely strong in critical thinking as well.

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This entire conversation is out of my league.   I just wanted to share in reference to the bolded that Foerster alg 1 had an entire chapter dedicated to exponents, including negative exponents.   Just sharing in case others reading this thread feel like they are going to need to abandon all non-CC textbooks.   Foerster is definitely strong in critical thinking as well.

 

Same goes for the Dolciani Algebra 1 that I have.  Am I oversimplifying things, or does it seem that the math programs often considered rigorous and used by homeschoolers (AOPS, Foerster, Dolciani, etc) will have no problem fitting to the Common Core standards?

 

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The CCSS line about negative exponents was from the MATH 8  not the high school standards...  Currently this is introduced in Algebra 1 (better texts like Foerster/Lial have decent sections over it)--then it is expanded with more meaning in Algebra 2.  With the common core this is now an 8th grade math topic-- again MUCH of Algebra 1 is now being pushed down to Math 8 to make room for the additional topics. 

 

The additional topics are more than just a few days spent on probability and statistics-- the Common Core is integrating at least a full semester of each of these into the traditional 'Algebra 1, Geometry and Algebra 2' progression... to make room MUCH of Algebra 1 is being pushed down to middle school math with Math 8 being very Algebra 1 heavy (lots of linear equations, solving problems with 2 variables by graphing, substituition and elimination and many more topics that are now to be taught fully instead of 'introduced'--- the introduction is in grades 6 and 7.

 

Right now it seems that students who use the traditional progression (this means older textbooks for Algebra 1, Geometry and Algebra 2) should add in something similar to AOPS Counting and Probability and then a high school Statistics course BEFORE the student is the age to take the ACT/SAT tests ... Currently very few US high school students take a Statistics class in high school-- the Common Core is being funded/promoted by the business industry and thus their adjenda must be included! 

 

Ideally this would look like:

6th and 7th grade  Pre-Algebra and something like AOPS Counting and Probability

8th grade --Algebra 1

9th grade-- Geometry

10th grade Algebra 2 with Trig--(beyond rt triangles-- close to full high school course)

11th grade Statistics 

 

Students would be prepared for the college entrance tests by the end of 11th grade.

 

I

 

Currently about 34% of US 8th graders are enrolled in a traditional Algebra 1 course.  The Common Core will now dictate that 100% of students take Algebra 1 in 7th or 8th grade-- but instead of calling the course 'Algebra 1' it will now be called Math 8. 

 

I have an eerie feeling that those tests (since they are being created by the very forces--people-- who are in charge of deciding the Common Core) will become the driving force for future curriculum.  Publishers will be forced to align their products to those tests so students will be 'prepared' at the proper time. 

 

Many of the Common Core proponents admit that it will take a full scholastic generation to implement (full K-11 sequence).  Students who are currently in middle school will have the hardest transition. 

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Same goes for the Dolciani Algebra 1 that I have.  Am I oversimplifying things, or does it seem that the math programs often considered rigorous and used by homeschoolers (AOPS, Foerster, Dolciani, etc) will have no problem fitting to the Common Core standards?

 

 

Those programs are still lacking in Statistics and advanced probablity.

 

The whole Common Core movement is based on resetting the foundation of Mathmatics in the US.  Our current curriculum-- including FOERSTER/Dolciani/Lia--l do not contain the same concepts (number theory/probablity/statistics) at the same level as other countries.  AOPS has more modeling, application, and probability-- if their Counting and Probility text is used-- but is still lacking in the area of statistics.

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Another poster brought up one of the biggest areas that troubles me-- the Common Core standards do not dictate what order concepts are to be taught in high school and relinquishes that decision to others.  The Common Core outlines what needs to be covered in Math 1, Math 2 and Math 3 COMBINED (leaving the Sr year open for a math elective or as a 'catch up year').

 

With out a formal break down by year, students who move from one district to another will have HUGE gaps!

 

 

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Ack!  I have not worried myself too much over Common Core but this is making my head hurt.  My 10th grader will be ok.  He already has decent ACT scores.  My 5th grader is strong in math and we can probably work his sequence out to fit.  But my poor 8th grader...he is not strong in math and is easily discouraged but is definitely college bound.  He will be taking these new SATs and there is no way he can get in all that math.

 

I realize all the other kids his age will be caught in transition, too.  It just is frustrating.  Maybe there will be a really generous curve in the early years where lots of kids have been caught in the middle. Ugh.

 

 

 

 

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Those programs are still lacking in Statistics and advanced probablity.

 

The whole Common Core movement is based on resetting the foundation of Mathmatics in the US.  Our current curriculum-- including FOERSTER/Dolciani/Lia--l do not contain the same concepts (number theory/probablity/statistics) at the same level as other countries.  AOPS has more modeling, application, and probability-- if their Counting and Probility text is used-- but is still lacking in the area of statistics.

 

Are you sure about that?   Foerster has a lot of probability covered in alg 1.  I don't remember much stats or number theory, but there is definitely significant coverage of probability.

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This entire conversation is out of my league.   I just wanted to share in reference to the bolded that Foerster alg 1 had an entire chapter dedicated to exponents, including negative exponents.   Just sharing in case others reading this thread feel like they are going to need to abandon all non-CC textbooks.   Foerster is definitely strong in critical thinking as well.

 

Thanks for checking on that. I thought ds had covered them when we did Algebra 1, but was too lazy to go look at my text. I have this phobia about giving up the first volume of Foerster until ds is safely off to college. :tongue_smilie:

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Are you sure about that?   Foerster has a lot of probability covered in alg 1.  I don't remember much stats or number theory, but there is definitely significant coverage of probability.

 

I dug out my copy of Foerster's Algebra 1 (yes I'm a math text nerd/collector!).  Chapter 8 does have 2 lessons on probability and 2 lessons on linear functions/scatter plots-- not significant according to the demands of the Common Core.

 

Foerster's Algebra 2 with Trigonometry has more on probablity (chapter 12)-- it comes fairly close to the Common Core standards. I think Foerster's Algebra 2 comes closer to the the Common Core than any other common US text in this area. 

 

 

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I do not think that we (homeschool community included) necessarily need to abandon our current texts-- but we will need to supplement until the progression shift is complete. 

 

I do not think it will be as simple as self-teaching through a test prep book.  The Common Core is much more than a few additional concepts--what most of the above discussion has been about simply because it is the easiest part to adjust to-- the Common Core is about a HUGE movement to radically change the way ALL Math is taught in the US. 

 

I'm enjoying this dialogue-- much easier to ponder things when you have others around to share their imputs!

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Jann, I just wanted to pipe in to say thank you for this discussion! As the parent of a 6th grader, this has been on my mind a lot, too.  I really appreciate you articulating the "ideal" progression as including C&P then statistics.  And if the student follows the progression you laid out they could do Calculus in 12th, yes?  I had been thinking dd would do Statistics in 12th, but what I am hearing is that you think there will be enough focus on those topics in the future ACT/SAT that it makes sense to do Stat in 11th grade, am I right?

 

(this is copied from Jann's post above)

6th and 7th grade  Pre-Algebra and something like AOPS Counting and Probability

8th grade --Algebra 1

9th grade-- Geometry

10th grade Algebra 2 with Trig--(beyond rt triangles-- close to full high school course)

11th grade Statistics 

 

 

It is my understanding that AoPS suggests you do the Intro Algebra book before Intro Counting & Probability . . . or maybe at least the first half of Intro Algebra? Can anyone confirm whether the student can do C&P between PreA & Algebra, or if they need to complete Alg 1 first?

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The CCSS line about negative exponents was from the MATH 8  not the high school standards...  Currently this is introduced in Algebra 1 (better texts like Foerster/Lial have decent sections over it)--then it is expanded with more meaning in Algebra 2.  With the common core this is now an 8th grade math topic-- again MUCH of Algebra 1 is now being pushed down to Math 8 to make room for the additional topics. 

 

Jann, how developmentally ready will the majority of students be to handle this transition? I guess I am thinking of the wide variation with my three children as to who was ready to handle more abstract concepts at which ages.

 

The additional topics are more than just a few days spent on probability and statistics-- the Common Core is integrating at least a full semester of each of these into the traditional 'Algebra 1, Geometry and Algebra 2' progression... to make room MUCH of Algebra 1 is being pushed down to middle school math with Math 8 being very Algebra 1 heavy (lots of linear equations, solving problems with 2 variables by graphing, substituition and elimination and many more topics that are now to be taught fully instead of 'introduced'--- the introduction is in grades 6 and 7.

 

Right now it seems that students who use the traditional progression (this means older textbooks for Algebra 1, Geometry and Algebra 2) should add in something similar to AOPS Counting and Probability and then a high school Statistics course BEFORE the student is the age to take the ACT/SAT tests ... Currently very few US high school students take a Statistics class in high school-- the Common Core is being funded/promoted by the business industry and thus their adjenda must be included! 

 

Thank you for posting this as well. It is my greatest struggle with the Common Core - that it is first, and foremost, a business - and a lucrative one at that. It is an educational system second at best.

 

Ideally this would look like:

6th and 7th grade  Pre-Algebra and something like AOPS Counting and Probability

8th grade --Algebra 1

9th grade-- Geometry

10th grade Algebra 2 with Trig--(beyond rt triangles-- close to full high school course)

11th grade Statistics 

 

Students would be prepared for the college entrance tests by the end of 11th grade.

 

I

 

Currently about 34% of US 8th graders are enrolled in a traditional Algebra 1 course.  The Common Core will now dictate that 100% of students take Algebra 1 in 7th or 8th grade-- but instead of calling the course 'Algebra 1' it will now be called Math 8. 

 

I have an eerie feeling that those tests (since they are being created by the very forces--people-- who are in charge of deciding the Common Core) will become the driving force for future curriculum.  Publishers will be forced to align their products to those tests so students will be 'prepared' at the proper time. 

 

Many of the Common Core proponents admit that it will take a full scholastic generation to implement (full K-11 sequence).  Students who are currently in middle school will have the hardest transition. 

 

At one point, our swim club decided that they were going to do things better than everyone else. Our swimmers swam hard, worked harder, and won everything.We had a huge pool of talent, which my oldest was smack in the middle of. Her freshman year, the thing kind of fell apart. The club was still very good with very good swimmers, but there were far too many damaged bodies to count. It was all too hard, too fast, and not developmentally appropriate. One thing that haunts me is the memory of the pit in my stomach "knowing" that this couldn't be right and yet, the coaches were the "experts." We let them lead even when we instinctively "knew" better.

 

Common Core leaves me with the same pit in my stomach. I am not sure whether the "experts" we are following are educators or businessmen with a heavy stake in the profit.

 

It's good to talk about how to work with the transition time, because this affects nearly all of us.

 

 

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It's good to talk about how to work with the transition time, because this affects nearly all of us.

 

 

 

Honestly, Lisa, I'm not going to change one iota of what we do.   My kids have all been far more than prepared for college level work and I am more than content with what they do.   The CC standards don't really make an impression on me one way or another b/c I never gave a hoot to what was being taught in ps to begin with and the SAT/ACT are something we simply do but don't educate around.

 

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It is my understanding that AoPS suggests you do the Intro Algebra book before Intro Counting & Probability . . . or maybe at least the first half of Intro Algebra? Can anyone confirm whether the student can do C&P between PreA & Algebra, or if they need to complete Alg 1 first?

 

You do need some algebra for C&P.

A traditional program or the first half of AoPS intro to Algebra is sufficient; you do not need to cover the entire Intro to Algebra text before C&P.

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Honestly, Lisa, I'm not going to change one iota of what we do.   My kids have all been far more than prepared for college level work and I am more than content with what they do.   The CC standards don't really make an impression on me one way or another b/c I never gave a hoot to what was being taught in ps to begin with and the SAT/ACT are something we simply do but don't educate around.

 

 

That pretty much sums up my attitude as well.

I refuse to worry at this point when not even clear is which changes will be implemented in testing. It will work out fine.

(And an overhaul of the US math instruction in schools was long overdue.)

 

ETA: It seems pretty certain to me that they won't roll out a test that tests things most schools have not yet taught, because a mass failure of the entire student population would have a negative backlash first and foremost for the testing company, the College Board. They won't benefit from a massive failure, so they will ensure it does not happen because it would be bad for business. I expect changes to be gradual.

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Taking a look at the 8th grade standards, while there may be some traditionally alg 1 content (linear equations and systems of equations), I don't see quadratics.  Also, I do not see simplifying radicals there in the 8th grade section as I think is mentioned above - did I miss it?  I see where it talks about perfect squares and knowing that sqrt of 2 is irrational.

 

It seems to me that perhaps a portion of alg 1 content may be pushed down to 8th (systems of equations being the standout topic in my own mind and maybe the distance formula in the coordinate plane).  Without inequalities and quadratics, I'm not sure it's the entirety of what has traditionally been alg 1.  Am I wrong?  Could we instead say that the "first half" of alg 1 is in the 8th grade standards?

 

I can't help but have a whole lot of negative thoughts about how CC will affect PS students.  (I'm not sure what it means for private school students, as I'm tentatively planning for my kids)  From Jann's description, it sounds like the standards are broader than current ones - I feel like I read conflicting opinions on that - and it will be a wonder if anyone in PS gets to calc by senior year.  Mostly, the standards seem unrealistic considering the current state of elementary math instruction leading into these 8th grade goals for average students.

 

The other thing I'm thinking is that stronger standards don't necessarily equate with depth.  I wouldn't be surprised if these topics could be taught in a shallow way with quite simple equations and such.

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Currently about 34% of US 8th graders are enrolled in a traditional Algebra 1 course.  The Common Core will now dictate that 100% of students take Algebra 1 in 7th or 8th grade-- but instead of calling the course 'Algebra 1' it will now be called Math 8. 

 

 

Are you saying you think Algebra 1 will only be taken by 9th graders and 8th graders will have what was traditionally known as Algebra 1 but it isn't considered that anymore?

 

Isn't this an implementation thing though? Meaning different schools/districts/states will do things differently. Our district has had many meetings but nothing like this has ever been brought to the table.

 

I'm in a state that has basically fully implemented CC except for all of the testing (some testing has been updated), which is on schedule to be done by next school year. My dd is currently in Algebra 1 in 8th grade. The school has not hinted at doing away with it, and they've actually added more Algebra 1 Honors classes this year for 7th/8th graders. It is considered a high school credit as long as she passes the EOC exam (our district had 900 8th graders taking it last year and a 99% passing rate).

 

Both of my dds start ps here in middle school, which is 6th through 8th, and it's been during a time when they have been implementing all of CC. They have not had that much of a problem.

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No worries here about common core. I saw first hand what the imposed graduation requirement of passing Algebra 2 did to the rigor of the math courses in the school district I taught in. In order to get the kids to graduate they dumbed down the math curriculum or have the potential to lose funding with the possibility of the state taking over the school because of the high drop out rate. It seems to me, with common core, they are trying to beef up what is being taught which is a good thing if Americans are going to be able to compete globally for jobs.

 

I feel that what one learns is far bigger than what can be measured on a test. Do the best you can and enjoy the opportunities you have with your children.

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I agree that the new standards, as you've presented them as I haven't read them in detail myself, sound like a good change.  I think it's ironic that Saxon recently came out with their separate algebra and geometry texts.  It sounds like the 3rd edition integrated texts would fit the new standards nicely.  Probability is incorporated as are some other topics not normally included.  I have no idea if they contain all of the "new" content or not.  I know Saxon doesn't work for all students, but I wouldn't be surprised if schools are giving it a look.   

 

I was happy to read on this thread that several people think that Saxon may work well with Common Core standards.  I have had the same thought ever since I first read a bit about the CC, and I was happy to hear of a student I know who placed into CC math II after completing Saxon Algebra I at home.  Although from what I hear on this thread, perhaps that standard 9th grade CC Math I class was not yet up to par, if Saxon Algebra I prepared the student for the 10th grade CC Math II class. I imagine it will take a few years to have the CC Math I, II and III classes be at the level they are projected to be, rather than the old standard. 

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ETA: It seems pretty certain to me that they won't roll out a test that tests things most schools have not yet taught, because a mass failure of the entire student population would have a negative backlash first and foremost for the testing company, the College Board. They won't benefit from a massive failure, so they will ensure it does not happen because it would be bad for business. I expect changes to be gradual.

Since I reside in a grades crazy area, it is more likely that the local schools would just buy the latest test prep books every year for SAT/ACT/PSAT and prep their students for it.  So there would be a reshuffling of topics being taught by the teachers based on the teachers assessment of the newest test prep materials. 

My kids are public school kids in the online school and their math modules were shuffled around every year to make sure the "correct" modules are covered by the time state testing comes around in April.  In fact both my boys have an extra math module/chapter this year just to make their math common core compliant.

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Rose, my son did C&P at age 12, so 7th grade I think, and he found it very tricky. Each concept was straight forward in isolation but when the review problems (and challengers!) integrated concepts from previous chapters he got quite muddled. So given my ds's special ability in math, I would be hesitant to recomend it to a 7th grader. Perhaps without the challengers, and definitely with the first half of aops intro algebra it could be doable, but I just thought you should be aware of our experience.

 

Ruth in NZ

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Rose, my son did C&P at age 12, so 7th grade I think, and he found it very tricky. Each concept was straight forward in isolation but when the review problems (and challengers!) integrated concepts from previous chapters he got quite muddled. So given my ds's special ability in math, I would be hesitant to recomend it to a 7th grader. Perhaps without the challengers, and definitely with the first half of aops intro algebra it could be doable, but I just thought you should be aware of our experience.

 

Ruth in NZ

Dd also did C&P at age 12 (also a very mathy student who would only study maths all day if I allowed). She hit a really hard patch about 3/4 of the way through the book and only did the in-section problems and exercises, skipping those review and challenge problems.

 

Ds, a comp sci major now taking grad level courses at his university, says he didn't touch some of the C&P topics until last year, his sophomore year!

 

NT is a piece of cake, comparatively speaking

 

Our plan is for dd to take the AoPS online C&P course at some point in the next 18 months.

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Another poster brought up one of the biggest areas that troubles me-- the Common Core standards do not dictate what order concepts are to be taught in high school and relinquishes that decision to others.  The Common Core outlines what needs to be covered in Math 1, Math 2 and Math 3 COMBINED (leaving the Sr year open for a math elective or as a 'catch up year').

 

With out a formal break down by year, students who move from one district to another will have HUGE gaps!

 

The order doesn't matter.  The students aren't expected to be in attendance for consecutive units. Districts here have had migrants for decades, as well as those who go back to the home country/territory for six to twelve weeks a year or bounce between whoever has custody this month.  The gaps are expected, and the way CC is laid out, it looks to me like they will be covered as usual. Threads will be picked up where the student left off, units with low priority will be omitted.  The procedure here is for the student to be placed in a double period math class, from Grade 6 on; for preK-5 they have rTi pullouts or pushins. That second period is used for the units the student needs to make up, whether they failed previously or never attempted. Oftentimes it is a group lesson, but sometimes not. Regents' Exams are offered in August, so they have summer school available for make-up as well.

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I was just coming to post about a concern that I have about math textbooks when I saw this thread.  Like many of you, I have my shelf full of the oldies but goodies of math textbooks.  DS2 is working his way through a 1960's version of Dolciani this year.  My concerns is that as these books become more and more scarce or go out of print like Jacobs, what do I tell the young moms coming up behind me who ask about which texts to use.  I am especially wondering in light of Jann's issues raised about the Common Core.  Let's assume that the next generation may not have the oldies but goodies.  What would you recommend now?

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I do not think that we (homeschool community included) necessarily need to abandon our current texts-- but we will need to supplement until the progression shift is complete. 

 

I do not think it will be as simple as self-teaching through a test prep book.  The Common Core is much more than a few additional concepts--what most of the above discussion has been about simply because it is the easiest part to adjust to-- the Common Core is about a HUGE movement to radically change the way ALL Math is taught in the US. 

 

I'm enjoying this dialogue-- much easier to ponder things when you have others around to share their imputs!

 

Would adding something like this to a tried and true algebra program help?

 

http://www.rainbowresource.com/searchspring.php?q=on+core+mathematics

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What does this mean for PSAT, ACT, and SATs in the short term?  Aren't they changing them as early as next year? 

 

I recently saw an announcement that the SAT would be revised in 2016 and the PSAT in 2015. This is a one year delay in putting out the revised tests.

 

The article in www.insidehighered.com said that the additional information would be available in the spring.

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From what it sounds like to me, although the common core may be more rigorous compared to what is taught in some schools currently, it is still far below the standards many people on this board have for their children.  Professor Jason   Zimba, who was the lead writer of the mathematics portion of common core, stated: “If you want to take calculus your freshman year in college, you will need to take more mathematics than is in the Common Core.† Here is the link to the paper: http://www.uaedreform.org/wp-content/uploads/2000/01/ZimbaMilgramStotskyFinal.pdf

 

In this video by Marc Tucker at the National Center on Education and the Economy, Tucker reports:

“Mastery of Algebra II is widely thought to be a prerequisite for success in college and careers. Our research shows that that is not so… Based on our data, one cannot make the case that high school graduates must be proficient in Algebra II to be ready for college and careers. The high school mathematics curriculum is now centered on the teaching of a sequence of courses leading to calculus that includes Geometry, Algebra II, Pre-Calculus and Calculus. However, fewer than five percent of American workers and an even smaller percentage of community college students will ever need to master the courses in this sequence in their college or in the workplace… they should not be required courses in our high schools. To require these courses in high school is to deny to many students the opportunity to graduate high school because they have not mastered a sequence of mathematics courses they will never need. In the face of these findings, the policy of requiring a passing score on an Algebra II exam for high school graduation simply cannot be justified.† Here is a link to the video: http://www.ncee.org/college-and-work-ready/  Later in the video he talks about how Common Core embraces these ideas.

 

 

So I am now wondering how much of Algebra II is really going to be tested, let alone topics traditionally covered in precalculus.  I want my children to do well on standardized tests, but I also have the goal that my children will take calculus in high school.  My dd is going back to Saxon next year (we were already planning on doing two years of Algebra I and she has requested to move back to Saxon).  So an integrated program might be the better fit to allow for statistics and calculus since she will only be in 8th grade next year.

 

 

 

 

 

 

 

 

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