AP Statistics as a 10th grade elective

[Anonymous]

Anonymous wrote:

Anonymous wrote:I teach AP Stats at an IB school.

Yes, AP Stats is frequently taken as an elective before starting the IB sequence (at my school you take IB Analysis 1 followed by IB analysis 2, so keeping those two courses together is ideal). The only prerequisite for the course is algebra 2.

The prior posters have a bit of misinformation in their comments. There is no calculus, it is taught from a purely algebraic/conceptual standpoint, and honestly the kids who have already taken calculus have a tougher time with stats because they want to spit out straight calculations and stats is more logic/interpretation than calculation. It is a very conceptual course. The kids who go back to IB from AP stats tend to write very strong IAs.

The super strong math kids honestly have a hard time with stats because it feels "fluffy" to them. It's a logic course with an undertone of math, but it's not pure calculations.

It "feels" fluffy?? Well, Duh Sherlock, of course it's highly fluffy without calculus, and by extension, without a hint of how any of the formulas are derived! I counter your claim that "they want to spit out straight calculations"; the strong math students actually want to see at least some proofs and derivations, especially if they've taken calculus. So yes, the class IS fluffy, because you can't just handwave stuff and call it "logic" without actually covering some of the math behind it! You see the logic there?

No, it feels “fluffy” because there is a whole unit without numbers. We talk about sampling methods, designing experiments, bias. Kids say it’s like a psychology class that gets you a math credit.

It feels “fluffy” because every answer requires a sentence to give context and relevance. It’s not enough to say the standard deviation of the random variable is 2.4. They are required to state, “The number of shots to make a basket typically varies by 2.4 from a mean of 5.1”. Kids say it feels like we spend as much time on vocabulary as calculations.

It feels “fluffy” because during probability the best strategies are to draw pictures (Venn diagrams, tables, trees) vs using formulas. The kids say it feels like they’re cheating.

It feels “fluffy” because there are so many conditions that have to be checked for inference, and conclusions are a whole paragraph. They claim to write more in an average stats class third quarter than they do in an average English class.

It feels “fluffy” because kids are expecting weekly problem sets of wrote calculations, and they end up with only a couple of those over the year.

I’m sorry that the class isn’t calculus based. It is designed that way on purpose to make it accessible to as many kids as possible. I’d say that’s a good thing in a world where we want the general populous to understand where data comes from and what studies are claiming.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I teach AP Stats at an IB school.

Yes, AP Stats is frequently taken as an elective before starting the IB sequence (at my school you take IB Analysis 1 followed by IB analysis 2, so keeping those two courses together is ideal). The only prerequisite for the course is algebra 2.

The prior posters have a bit of misinformation in their comments. There is no calculus, it is taught from a purely algebraic/conceptual standpoint, and honestly the kids who have already taken calculus have a tougher time with stats because they want to spit out straight calculations and stats is more logic/interpretation than calculation. It is a very conceptual course. The kids who go back to IB from AP stats tend to write very strong IAs.

The super strong math kids honestly have a hard time with stats because it feels "fluffy" to them. It's a logic course with an undertone of math, but it's not pure calculations.

It "feels" fluffy?? Well, Duh Sherlock, of course it's highly fluffy without calculus, and by extension, without a hint of how any of the formulas are derived! I counter your claim that "they want to spit out straight calculations"; the strong math students actually want to see at least some proofs and derivations, especially if they've taken calculus. So yes, the class IS fluffy, because you can't just handwave stuff and call it "logic" without actually covering some of the math behind it! You see the logic there?

No, it feels “fluffy” because there is a whole unit without numbers. We talk about sampling methods, designing experiments, bias. Kids say it’s like a psychology class that gets you a math credit.

It feels “fluffy” because every answer requires a sentence to give context and relevance. It’s not enough to say the standard deviation of the random variable is 2.4. They are required to state, “The number of shots to make a basket typically varies by 2.4 from a mean of 5.1”. Kids say it feels like we spend as much time on vocabulary as calculations.

It feels “fluffy” because during probability the best strategies are to draw pictures (Venn diagrams, tables, trees) vs using formulas. The kids say it feels like they’re cheating.

It feels “fluffy” because there are so many conditions that have to be checked for inference, and conclusions are a whole paragraph. They claim to write more in an average stats class third quarter than they do in an average English class.

It feels “fluffy” because kids are expecting weekly problem sets of wrote calculations, and they end up with only a couple of those over the year.

I’m sorry that the class isn’t calculus based. It is designed that way on purpose to make it accessible to as many kids as possible. I’d say that’s a good thing in a world where we want the general populous to understand where data comes from and what studies are claiming.

You misunderstand a bit what the argument is. What makes a great course is building connections between concepts, often through a mathematical derivation to show the logic behind how things work. Starting with the normal distribution, ie half the class, the fundamental ideas are underpinned by calculus, nothing can change that. The skill as a teacher is to condense those principles into accessible information that even the 10th grader can understand so you’d have to introduce some calculus concepts. That doesn’t mean the class is calculus based, or that it needs to take too much class time.

Almost all examples you give are because of compartmentalization of concepts. Experimental design, sampling and bias are introduced because of how they affect ‘numbers’ like the mean, it’s straightforward and more educational to find examples that are more quantitative.

Formulaic sentences like ‘The number of shots to make a basket typically varies by 2.4 from a mean of 5.1’ is what makes the class fluffy, and I’m not sure I even agree, the language is too imprecise, what do you mean by ‘typical’ and ‘varies’. You could literally use the same exact sentence for other measurements of spread like inter quartile range, mean absolute deviation, range etc

Theres nothing fluffy about Venn diagrams and decision trees. Tables are a way to summarize data.

Theres a real teaching deficit in how to write a mathematical exposition, I’ll give you that. Students should know how to write a mathematical argument that involves sentences, equations, logic and make it easy to understand and read, it can be more concise than long paragraphs, but it’s still a skill that’s mostly undeveloped. The conditions for inferences are driven by logic, but that doesn’t come through if they are presented as a check list used to decide what formula to pick.

The calculations are there, but are glossed over, it comes down to choosing the relevant examples and exercises.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:I teach AP Stats at an IB school.

Yes, AP Stats is frequently taken as an elective before starting the IB sequence (at my school you take IB Analysis 1 followed by IB analysis 2, so keeping those two courses together is ideal). The only prerequisite for the course is algebra 2.

The prior posters have a bit of misinformation in their comments. There is no calculus, it is taught from a purely algebraic/conceptual standpoint, and honestly the kids who have already taken calculus have a tougher time with stats because they want to spit out straight calculations and stats is more logic/interpretation than calculation. It is a very conceptual course. The kids who go back to IB from AP stats tend to write very strong IAs.

The super strong math kids honestly have a hard time with stats because it feels "fluffy" to them. It's a logic course with an undertone of math, but it's not pure calculations.

It "feels" fluffy?? Well, Duh Sherlock, of course it's highly fluffy without calculus, and by extension, without a hint of how any of the formulas are derived! I counter your claim that "they want to spit out straight calculations"; the strong math students actually want to see at least some proofs and derivations, especially if they've taken calculus. So yes, the class IS fluffy, because you can't just handwave stuff and call it "logic" without actually covering some of the math behind it! You see the logic there?

No, it feels “fluffy” because there is a whole unit without numbers. We talk about sampling methods, designing experiments, bias. Kids say it’s like a psychology class that gets you a math credit.

It feels “fluffy” because every answer requires a sentence to give context and relevance. It’s not enough to say the standard deviation of the random variable is 2.4. They are required to state, “The number of shots to make a basket typically varies by 2.4 from a mean of 5.1”. Kids say it feels like we spend as much time on vocabulary as calculations.

It feels “fluffy” because during probability the best strategies are to draw pictures (Venn diagrams, tables, trees) vs using formulas. The kids say it feels like they’re cheating.

It feels “fluffy” because there are so many conditions that have to be checked for inference, and conclusions are a whole paragraph. They claim to write more in an average stats class third quarter than they do in an average English class.

It feels “fluffy” because kids are expecting weekly problem sets of wrote calculations, and they end up with only a couple of those over the year.

I’m sorry that the class isn’t calculus based. It is designed that way on purpose to make it accessible to as many kids as possible. I’d say that’s a good thing in a world where we want the general populous to understand where data comes from and what studies are claiming.

You misunderstand a bit what the argument is. What makes a great course is building connections between concepts, often through a mathematical derivation to show the logic behind how things work. Starting with the normal distribution, ie half the class, the fundamental ideas are underpinned by calculus, nothing can change that. The skill as a teacher is to condense those principles into accessible information that even the 10th grader can understand so you’d have to introduce some calculus concepts. That doesn’t mean the class is calculus based, or that it needs to take too much class time.

Almost all examples you give are because of compartmentalization of concepts. Experimental design, sampling and bias are introduced because of how they affect ‘numbers’ like the mean, it’s straightforward and more educational to find examples that are more quantitative.

Formulaic sentences like ‘The number of shots to make a basket typically varies by 2.4 from a mean of 5.1’ is what makes the class fluffy, and I’m not sure I even agree, the language is too imprecise, what do you mean by ‘typical’ and ‘varies’. You could literally use the same exact sentence for other measurements of spread like inter quartile range, mean absolute deviation, range etc

Theres nothing fluffy about Venn diagrams and decision trees. Tables are a way to summarize data.

Theres a real teaching deficit in how to write a mathematical exposition, I’ll give you that. Students should know how to write a mathematical argument that involves sentences, equations, logic and make it easy to understand and read, it can be more concise than long paragraphs, but it’s still a skill that’s mostly undeveloped. The conditions for inferences are driven by logic, but that doesn’t come through if they are presented as a check list used to decide what formula to pick.

The calculations are there, but are glossed over, it comes down to choosing the relevant examples and exercises.

Spot on observations. One of the crux issues is that students have not built enough mathematical maturity to make their arguments more precise and cohesive so that they can be unambiguously understood. While it's not a requirement to write a mathematically rigorous proof/argument at this level (certainly not with calculus), it should be a requirement to focus on improving their mathematical exposition so that the logic can shine through, and doing that without making assumptions and arbitrary statements (as the PP pointed out above). An introductory statistics class is a good time to do that, but honestly this skill could have slowly been honed from as early as elementary school if the curriculum and the teaching was done appropriately. Even young students can write nice mathematical arguments to show why the sum of even numbers is always even, why the product of all odd numbers is always odd, etc. Young students have reasoning skills, but they are not taught to develop them in the context of mathematics, which is highly unfortunate. Lacking this skill very often leads to deep misunderstandings at the high school level, affecting not just just students but regrettably many teachers as well.

[Anonymous]

Reviving this as a cautionary tale. My child is taking Precalculus and AP Statistics at the same time, AP statistics is by far harder, and it’s mostly because it lacks the calculus foundation to really understand the material. The teacher is supposedly good being an AP Statistics grader for many years. This is the first time I’ve seen teaching to the test in earnest. The entire class is taught through examples one might encounter in the AP Statistics exam, and there’s zero explanation on why things work the way they do, no background, no derivations, just a stream of formulas to apply. I also suspect the teacher herself doesn’t really understand the material well, graphs shown without labels on x and y, but somehow it should be obvious the probability is the area under the curve. The mathematical language is atrocious, she uses “density curve” instead of probability density (distribution) function etc. never seen a formal definition of what the cumulative distribution function is etc.

My son is doing well in Precalculus, but struggling a lot in AP Statistics. I would definitely recommend taking it after Calculus. By now it’s quite clear he won’t do well on the AP exam.

[Anonymous]

I guess my kid is the reverse of the previous poster's. She took AP Stats in 10th grade at RMIB, concurrently with honors precalc, which she had to drop down to regular precalc because she was struggling with the pace. She did just fine in AP Stats, both gradewide and on the AP exam. She's a strong math student but not a superstar -- she went on to take Calc AB junior year and Calc BC senior year rather than the IB math classes. She took math SL rather than HL.

[Anonymous]

Anonymous wrote:I guess my kid is the reverse of the previous poster's. She took AP Stats in 10th grade at RMIB, concurrently with honors precalc, which she had to drop down to regular precalc because she was struggling with the pace. She did just fine in AP Stats, both gradewide and on the AP exam. She's a strong math student but not a superstar -- she went on to take Calc AB junior year and Calc BC senior year rather than the IB math classes. She took math SL rather than HL.

Probably it depends how the kid learns, but if you want to derive everything, then statistics is much harder then precalculus. If you understand situational nuances and can map easily scenarios with formulas, then statistics is easier than precalculus.

[Anonymous]

Anonymous wrote:Reviving this as a cautionary tale. My child is taking Precalculus and AP Statistics at the same time, AP statistics is by far harder, and it’s mostly because it lacks the calculus foundation to really understand the material. The teacher is supposedly good being an AP Statistics grader for many years. This is the first time I’ve seen teaching to the test in earnest. The entire class is taught through examples one might encounter in the AP Statistics exam, and there’s zero explanation on why things work the way they do, no background, no derivations, just a stream of formulas to apply. I also suspect the teacher herself doesn’t really understand the material well, graphs shown without labels on x and y, but somehow it should be obvious the probability is the area under the curve. The mathematical language is atrocious, she uses “density curve” instead of probability density (distribution) function etc. never seen a formal definition of what the cumulative distribution function is etc.

My son is doing well in Precalculus, but struggling a lot in AP Statistics. I would definitely recommend taking it after Calculus. By now it’s quite clear he won’t do well on the AP exam.

Have you taken a practice test? 70% earns a 5. 45% earns a 3. Struggling doesn't mean doing poorly on the exam.

https://www.coralgablescavaliers.org/ourpages/auto/2018/4/12/43682417/AP%20Stat%20Student%20ScoringSheet.pdf

[Anonymous]

Anonymous wrote:Reviving this as a cautionary tale. My child is taking Precalculus and AP Statistics at the same time, AP statistics is by far harder, and it’s mostly because it lacks the calculus foundation to really understand the material. The teacher is supposedly good being an AP Statistics grader for many years. This is the first time I’ve seen teaching to the test in earnest. The entire class is taught through examples one might encounter in the AP Statistics exam, and there’s zero explanation on why things work the way they do, no background, no derivations, just a stream of formulas to apply. I also suspect the teacher herself doesn’t really understand the material well, graphs shown without labels on x and y, but somehow it should be obvious the probability is the area under the curve. The mathematical language is atrocious, she uses “density curve” instead of probability density (distribution) function etc. never seen a formal definition of what the cumulative distribution function is etc.

My son is doing well in Precalculus, but struggling a lot in AP Statistics. I would definitely recommend taking it after Calculus. By now it’s quite clear he won’t do well on the AP exam.

This is how Statistics is taught in college for non math majors, and why most of published science is statistically unsound.
It's not a "math" class. It's an "research tools" class.


BTW, "Probability density curve" is standard but less popular terminology. "Curve" is a synonym for "graph of a function". You even wrote curve" in your own description of the graph!

Google "probability density curve"

[Anonymous]

Anonymous wrote:Reviving this as a cautionary tale. My child is taking Precalculus and AP Statistics at the same time, AP statistics is by far harder, and it’s mostly because it lacks the calculus foundation to really understand the material. The teacher is supposedly good being an AP Statistics grader for many years. This is the first time I’ve seen teaching to the test in earnest. The entire class is taught through examples one might encounter in the AP Statistics exam, and there’s zero explanation on why things work the way they do, no background, no derivations, just a stream of formulas to apply. I also suspect the teacher herself doesn’t really understand the material well, graphs shown without labels on x and y, but somehow it should be obvious the probability is the area under the curve. The mathematical language is atrocious, she uses “density curve” instead of probability density (distribution) function etc. never seen a formal definition of what the cumulative distribution function is etc.

My son is doing well in Precalculus, but struggling a lot in AP Statistics. I would definitely recommend taking it after Calculus. By now it’s quite clear he won’t do well on the AP exam.

It sounds like your son has a bad teacher, which can happen in any class. If he had a good teacher, you might be coming here to recommend the path to OP. I'm sorry he is having a tough time with a mediocre teacher. Is he meeting with a tutor to catch up?

[Anonymous]

Anonymous wrote:

Anonymous wrote:Reviving this as a cautionary tale. My child is taking Precalculus and AP Statistics at the same time, AP statistics is by far harder, and it’s mostly because it lacks the calculus foundation to really understand the material. The teacher is supposedly good being an AP Statistics grader for many years. This is the first time I’ve seen teaching to the test in earnest. The entire class is taught through examples one might encounter in the AP Statistics exam, and there’s zero explanation on why things work the way they do, no background, no derivations, just a stream of formulas to apply. I also suspect the teacher herself doesn’t really understand the material well, graphs shown without labels on x and y, but somehow it should be obvious the probability is the area under the curve. The mathematical language is atrocious, she uses “density curve” instead of probability density (distribution) function etc. never seen a formal definition of what the cumulative distribution function is etc.

My son is doing well in Precalculus, but struggling a lot in AP Statistics. I would definitely recommend taking it after Calculus. By now it’s quite clear he won’t do well on the AP exam.

This is how Statistics is taught in college for non math majors, and why most of published science is statistically unsound.
It's not a "math" class. It's an "research tools" class.


BTW, "Probability density curve" is standard but less popular terminology. "Curve" is a synonym for "graph of a function". You even wrote curve" in your own description of the graph!

Google "probability density curve"

Statistics is most definitely a math class, and it can be taught in many ways, some better are than others.

When you teach an introductory class you need to stick to clear and broadly used terms. “Density curve” is different from “probability density curve”. I did the google search you suggested, first ten hits take you to “probability density function”, which tells you what the actual standard is.

It’s true that curve usually means graph of a (nonlinear) function, but when you describe a uniform constant distribution by a “density curve”, and never defined what “density” is, it’s just confusing and odd. Again in sticking to widely used nomenclature, it’s common to say “area under the curve” not “area under the function”.

[Anonymous]

Anonymous wrote:

Anonymous wrote:Reviving this as a cautionary tale. My child is taking Precalculus and AP Statistics at the same time, AP statistics is by far harder, and it’s mostly because it lacks the calculus foundation to really understand the material. The teacher is supposedly good being an AP Statistics grader for many years. This is the first time I’ve seen teaching to the test in earnest. The entire class is taught through examples one might encounter in the AP Statistics exam, and there’s zero explanation on why things work the way they do, no background, no derivations, just a stream of formulas to apply. I also suspect the teacher herself doesn’t really understand the material well, graphs shown without labels on x and y, but somehow it should be obvious the probability is the area under the curve. The mathematical language is atrocious, she uses “density curve” instead of probability density (distribution) function etc. never seen a formal definition of what the cumulative distribution function is etc.

My son is doing well in Precalculus, but struggling a lot in AP Statistics. I would definitely recommend taking it after Calculus. By now it’s quite clear he won’t do well on the AP exam.

It sounds like your son has a bad teacher, which can happen in any class. If he had a good teacher, you might be coming here to recommend the path to OP. I'm sorry he is having a tough time with a mediocre teacher. Is he meeting with a tutor to catch up?

It’s probably true I would be recommending this path if he was doing well. You hear often that Statistics is easy, and that’s just not exactly true. I am taking over the tutoring part, wish I did it earlier.

[Anonymous]

Very common.