Teaching to Mastery and Pace

[Penguin]

I did not want to further derail this thread about participation with my questions about mastery, so I am making a new thread.

 

In middle school, we absolutely taught to mastery.  Now, in 9th grade, I can't wrap my head around doing it any differently - mastery is what makes sense to me.  

 

But when I read about those of you teaching to mastery, I often wonder if all of you have the type of student who usually (maybe always) gets things easily.  My son is bright but sometimes he gets really stuck on new concepts (usually in science), and we have to circle around and around and come in sideways until he really truly gets it.  

 

And that is when I panic over pace and what if we don't cover enough content? I would like him to be ready for an AP Science by 11th, or to be able to do well on an SAT Subject Test.  I had thought that maybe he would take the SAT Biology in June, but at the moment that seems like wishful thinking.  Pace is not the only limiting factor with regard to that test, but it is a factor.

 

What happens when mastery collides with pace?

(edited to make a better question!)

 

 

 

[EKS]

Yes and no.

 

My older son is 2E--gifted with dyslexia.  So he would either get something quickly or take forever.  Frequently he would appear to understand and even get As on tests but later on I would see that he hadn't really understood at all.  What worked best with him was circling back around from a different angle a few times.  In fact, I realized a few months ago that even though he was accelerated in math for most of his schooling, he did end up repeating just about every level in some form or another.  He is a kid who needs to see the big picture before he can truly understand.

 

My younger son is highly gifted.  He gets things at lightning speed--and forgets them almost as quickly.  So he also needs to come back around a few times to get whatever it is firmly rooted in his mind.

 

I do believe that there are different forms of mastery.  There is mastery in the moment--the kid completely gets whatever it is and can apply it, but then a few weeks or months or years later due to lack of practice or retrieval, it is gone--though I find that when we come back to whatever it is, it is easier to understand.  I teach history and science to this level of mastery, meaning that I don't get too worried about my kids remembering everything.

 

There is also mastery of the forever and ever type--where the kid is fully able to do or remember whatever it is forevermore.  I think that reading (to maybe a 5th or 6th grade level) and basic arithmetic (up to, but not including, fractions) tends to get taught to this level.  But beyond that, if you want this level of mastery, for most students, you have to consciously provide opportunities for practice or it gets lost.  For example, my younger son, who is halfway through Algebra II, only just last year truly mastered fractions, decimals, percents, and ratio/proportion.  Really.  And I think that doing algebra and geometry helped with that more than simply hammering away at the arithmetic would have.

 

So, yes, you do need to balance pace with mastery.  I do this by moving quickly when I can through the easy stuff.  I will also back off when it's not clicking and move on if I can and then circle back around when the time is right.

[katilac]

I said this in the other thread, in regards to moving on before mastery: One practical reason is that students sometimes hit a wall with a certain concept, but are able to grasp it the second time around with no problem if you take a break and come back to it.

 

It sounds like you are familiar with that and the 'working sideways.' I don't think it's a negative at all. 

 

I do think you have to balance mastery and pace, particularly in high school.

 

And what do we mean by mastery? To some people, it means having a high overall understanding of each chapter or section before moving on. To others, it means having a high understanding of every concept before moving on. 

 

The brightest of students are not going to master every single concept in every single subject, unless they are being vastly underchallenged in their courses. They can have a tentative or hazy handle on certain concepts while still doing very well overall. 

 

Of course it's great to try different approaches and circle back to topics at a later date, but I've also decided that it's okay if they move on without grasping every function detailed in the microbiology chapter, y'know? 

 

If we had stuck with Algebra 1 until dd mastered all the topics, we would have lost our minds. There were a few things she just was not getting. She moved on to Geometry and did great, then did Algebra 2 and precalc in a year and did great. 

 

Now, she earned a B in Algebra 1, so it wasn't a case of being completely lost, but she was lost on certain concepts. If she had kept banging her head against that wall, I think it would have killed her enjoyment of math, and we might have killed each other in the bargain. 

 

 

[Penguin]

Why, katilac...were you peeking into my homeschool and noticing DS struggling to grasp the nuances of microbiology? :lol:

[kiana]

I think there's a difference between not moving on in the sequence of knowledge and not moving on in any area. 

 

I can absolutely see that when a student is banging his head against the wall struggling on, say, quadratic equations, doing a sidestep and working on systems of linear equations for a while and then coming back (or vice versa) may be an excellent step. Neither of these is really a prerequisite for the other.

 

But it wouldn't make sense to move to either of these for a student who is struggling on linear equations. 

 

This is where the textbooks that have a chapter dependence tree in the beginning are VERY useful -- so you can see where you can skip around to easily. (example -- see page iv on this download -- http://abstract.ups.edu/download/aata-20120811.pdf)

[regentrude]

But when I read about those of you teaching to mastery, I often wonder if all of you have the type of student who usually (maybe always) gets things easily.  My son is bright but sometimes he gets really stuck on new concepts (usually in science), and we have to circle around and around and come in sideways until he really truly gets it.  

 

And that is when I panic over pace and what if we don't cover enough content? I would like him to be ready for an AP Science by 11th, or to be able to do well on an SAT Subject Test.  I had thought that maybe he would take the SAT Biology in June, but at the moment that seems like wishful thinking.  Pace is not the only limiting factor with regard to that test, but it is a factor.

 

What happens when mastery collides with pace?

 

I see no value in covering a fixed amount of content if it means rushing and mastery cannot be achieved.

Selecting the topics and amount what to cover has to take into account how much the student can master and understand. Important concepts must be absolutely mastered- less important topics can be presented for exposure. It requires subject expertise to discern which textbook chapters belong into which category.

In other subjects, material is not adjusted, just pace. I don't time math; we take whatever time is necessary to progress through the books in a linear fashion and achieve long term mastery (not just retention until the next chapter test)

 

The one time we encountered a mismatch between pace and mastery at home, we have opted to forgo subject testing when it was clear that we would not be able to cover everything that is tested well enough and have time to do test preparation. We abandoned the idea of the chemistry subject test a few months into the school year when it became clear that this would require more of an effort than either of us were willing to put into this particular class.

 

I prefer to teach the most important concepts thoroughly, even at the expense of covering the peripheral areas at all. In my college physics classes, I select the portions of the textbook I need my students to master and add a few sections that I want them to have seen for exposure. We go at a slow enough pace that the mastery of the basics can be achieved. To me, this is far more valuable than hustling to make sure we briefly touch every chapter of the book.

 

[3sapphires]

hmm. . . I'm listening.

 

I had just made the decision to circle back and hammer away at basic skills with my dd who is suposed to be doing Algebra 1, and is doing a good job with it mostly, but keeps getting little things wrong (and honestly a lot of these are careless errors.) Reading this thread, I am starting to think that I am just punishing her, and that is not my intent.

 

I think I will try to go back to the Algebra 1 book tomorrow and see how we do. Maybe I can throw in 15 minutes of Khan a day to keep those basic skills fresh, but still move on in content. . .

[Penguin]

regentrude, I have (at least temporarily) abandoned the SAT Bio test for the same reason.  I had promised DS a unit on Marine Bio within his 9th grade Bio course, and we are also doing an above-average amount of fieldwork.  Something had to give, and it was the test.  When we get closer to the end of the year, he can think about taking in in October and doing test prep over the summer. Or maybe we'll just wait it out and see if he takes an AP Chem or AP Bio down the road.

[Chrysalis Academy]

This is a great conversation. I've also struggled with designing a high school science course (Biology, at the moment) that will satisfy me, in terms of depth of coverage of key topics and pace, and that will also be test-prep material. Given the mile-wide inch deep nature of the tests, I'm not convinced that this is possible. I think I'd rather do the class I want to do, and then do focused test prep, rather than build a whole year's class around trying to cover every single thing that might show up on the test.

[swimmermom3]

This is a great conversation. I've also struggled with designing a high school science course (Biology, at the moment) that will satisfy me, in terms of depth of coverage of key topics and pace, and that will also be test-prep material. Given the mile-wide inch deep nature of the tests, I'm not convinced that this is possible. I think I'd rather do the class I want to do, and then do focused test prep, rather than build a whole year's class around trying to cover every single thing that might show up on the test.

 

If you write many of your own courses, I strongly suggest you look at several class syllabi from experienced teachers and professors. It doesn't take long to see which chapters in a particular text will get dropped.

 

The year we did chemistry at home, I quickly found out that there was no way that we could follow Dr. Tang's Honors Chemistry syllabus,do the full-scale labs we were doing, and be ready for the SAT Subject test at year's-end. In fact, there were a couple of times that we dropped down to a standard high school class level on a particular topic or dropped it altogether if it wasn't on the standard coursework. 

 

Dr. Tang's chemistry syllabi offer a good example of how you can adjust your work to meet your student. Because you have three different levels to choose from, you can pick and to choose to adjust if mastery requires more time than your original plan.

 

Have you seen Cheryl Massengale's amazing site: Biology Junction? 

 

Spend some time there and see if that helps with your pacing.