Math Pacing Wisdom?

[ShawnaB]

I feel like I'm re-learning how to teach math, and for the first time starting to recognize what true "mastery" of arithmetic is. I've seen and used so many curriculums that proport to be mastery-based, but I find that most actually are not, at least not without a lot of supplementation.

I'm now looking at the R&S 2 and 3 curriculum that is sitting in front of me that I plan to use with my small class of 5 2nd-graders and 2 3rd-graders. It is seeming blessedly simple. However, I do think that my 5 rising 2nd graders have pretty much covered most of the content, and could most likely do R&S 3 along with the 3rd graders.

My question: just because a child can move through arithmetic at a more accelerated paced, should they? Or, is there wisdom in repetition and doing math until it is so easy it is automatic?

Old me would have said yes...accelerate, accelerate, accelerate. But now I'm thinking maybe there is wisdom in repetition? Of math actually feeling a little "easy" and "familiar"?

So, any opinions? Should I put my 2nd graders through another year of content that we have basically already covered? Or, do I push them ahead because the can do more?

[buckeyelaw]

I do think there is wisdom in repetition, but I also think acceleration is fine in some circumstances. I began my current second grader with R&S 1 last year at the beginning of 1st grade. It was too slow for him and after about 3 weeks he was trying to push himself ahead by learning the higher addition/subtraction facts on his own. I decided to bump him up to R&S 2 and he is just now finishing up R&S 3 at the end of second grade. He knows his facts and I'm not concerned that we have moved too fast for him. R&S 2 took him through all of the multiplication and division facts up to 12 and he is just now starting a bit of simple long division (we have 3 weeks left). I think that if your students have their addition and subtraction facts down cold that you would be ok accelerating them.

[Michelle T]

Before you advance your student too far ahead know, too, that speed in recall of those facts is important. It is third grade when we begin the written speed drills with 100 facts. The goal for 3rd is 5 minutes, 4th graders have 4 minutes, 5th graders have 3 and 6th graders 2 minutes. We want those facts to be automatic. This can be attained only through consistent daily practice and review.

Something to consider.

[ShawnaB]

Thank you Buckeye and Michelle! Helpful perspectives.

Michelle, I am learning that most curriculums, although purporting to instill mastery, actually do not have enough practice built in to create that automaticity. I am hopeful that R&S may be the exception.

I started this year with Singapore and stopped after about 6 weeks. WAY too much complex problem solving with little to no mastery of facts. I then scrambled to create lessons from a variety of replacement unit studies, (Marilyn Burns, etc.) to teach number sense and place value, and printed about a bazillion fact practice worksheets from online generators to practice those addition facts, triples, missing numbers, etc. Imagine my delight in finding that R&S has all that done for me! I have searched for old fashioned drill practice sheets, and I think they may not exist anymore!

In December, I finally settled on Math U See as our core but still needed to supplement for fact practice. We did a lot of flashcard drilling as well. (This year, I was limited to purchasing secular math curriculum via a Charter School, or would have switched to R&S sooner.)

All that to say, my rising 2nd graders are doing pretty well with their addition and subtraction facts. But, they could still benefit from more practice. The two rising third graders have them mastered inside out and backward. And, they are conceptually ready for multiplication and division I believe, having a very solid grasp on place value, and easily adding and subtracting numbers into the 1000s with regrouping. The rising 2nd graders are conceptually not quite as solid. I am leaning towards having my 2nd graders do the Grade 2 level, even if somewhat easy for them.

Michelle...in a classroom setting, how much "sitting at the elbow" do you expect to do with primary students? In looking at the Grade 2 math, I would expect my students, with some initial instruction and review, would be able to complete their practice work fairly independently. Is that the idea?

[Michelle T]

The Rod & Staff Lessons are interactive so most of the time is at your elbow. Once the lesson part is done the student can be independent completing their workbook pages which should then only take them 5 to 10 minutes. This depends upon how efficiently you child works. When they are finished immediate feedback should be given so correction can then be completed.

I tell classes to spend 45 minutes to an hour on math but homeschool should be all done within 30.

[KikaMarie]

I tell classes to spend 45 minutes to an hour on math but homeschool should be all done within 30.

Is this also an appropriate amount of time for grade 5?

My further question has to do with my son who is a bit older than the children noted above - he is 12 and mid-way through the grade 5 book. I thought he was doing okay up until a few weeks ago. We started grade 4 in September and once he got familiar with the text, I moved him through the grade 4 book quickly by doing the chapters at one per week and then taking the tests. He was scoring in the 90s, but by the time he met long division with multiple digit divisors and multi-digit multiplication in the grade 5 book, he hit a wall of upset. I'm wondering where I should drop back to and how I should structure his lesson time for math. He doesn't have any trouble with any of the "concepts" that are covered so far, but the larger number multiplication and division really causes stress for him. He can recall facts when not stressed, but he is very upset about math now and so recall is very, very slow. We are also in the process of a psychological educational evaluation for him and we expect to learn something about his processing at our meeting this week. But some general math advice on "backing up" with him would be appreciated.

Monica

[bean]

Thank you Buckeye and Michelle! Helpful perspectives.

Michelle, I am learning that most curriculums, although purporting to instill mastery, actually do not have enough practice built in to create that automaticity. I am hopeful that R&S may be the exception.

I started this year with Singapore and stopped after about 6 weeks. WAY too much complex problem solving with little to no mastery of facts. I then scrambled to create lessons from a variety of replacement unit studies, (Marilyn Burns, etc.) to teach number sense and place value, and printed about a bazillion fact practice worksheets from online generators to practice those addition facts, triples, missing numbers, etc. Imagine my delight in finding that R&S has all that done for me! I have searched for old fashioned drill practice sheets, and I think they may not exist anymore!

Singapore does have lots math drill in the TE unless it had changed since we used it.

[Jen (formerly) in Japan]

I am learning that most curriculums, although purporting to instill mastery, actually do not have enough practice built in to create that automaticity. I am hopeful that R&S may be the exception.

You are beginning to see the difference between MASTERY and RECOGNITION. In the pedagogy of teaching, it is understood that there is a vast difference between the two concepts. Multiple choice tests, T/F, and even short answer are what is called "selected response" questions. In modern education, these types of assessments have become the norm, because face it, they are very easy to grade. Obviously they are primarily based on the recognition concept. Honestly, even "narration" the way most homeschoolers practice it is based on short-term knowledge and recognition.

IMO the genius of R&S math is that it *does* move slowly enough for the simply arithmetic concepts to sink in. Here's the hilarious part: your child could be cruising along in R&S math in November, hit a growth spurt over the holidays, and suddenly "can't remember" anything in January. But, resuming the mastery paced math lessons in R&S, he will be "reminded" that he actually does know his math.

The easy pacing and mastery basis of R&S math in ARITHMETIC the elementary years is purposeful. Your students should be working with speed drills and flash cards every day, and the time is built into there: 15 mins on facts, 20 mins on the written lesson. If not every day, the facts should be part of nearly every day. Getting put "on the spot" individually and uniquely is what eventually sharpens the student's resolve to master math facts. When my own kids were going through that stage, I built in a lot of positive reinforcements into learning math facts, everything from praise to rewards (for instance, a sticker for missing less than one fact, then 20 stickers = a small treat).

All that to say, you are beginning to recognize what makes MP's mastery based curricula different and unique from "all the others out there".





Jen

[ShawnaB]

but by the time he met long division with multiple digit divisors and multi-digit multiplication in the grade 5 book, he hit a wall of upset.

Monica

Monica, as I have supported a lot of older grammar/logic students through their math curriculum, long division is where many hit a wall. Long division requires automatic recall of all four arithmetic functions: addition, subtraction, multiplication, and division--just to work one problem. If those basic facts are not automatic--thus requiring almost zero energy to recall--I've found that students don't have a lot of mental energy left to go through the steps of actually solving a long division problem. They forget how and why they are doing the algorithm because too much energy is used up in doing all the basic arithmetic. It starts to feel really hard and overwhelming.

These realities were covered so well by the math speaker on the Soldalitas recording from last year....this isn't my original discovery by any means....but I have born witness to the truth of what she said.

So, if your son's recall of the addition, subtraction, multiplication and division facts are not totally automatic...even if they are like 80%....long division will be hard. It sounds like some of his recall issues may be stress induced, and I don't have any advice for helping in that way. But it sounds like you are seeking some professional input in that area, which is great, and hopefully, you'll come up with some strategies to reduce stress and increase memory. Hang in there!

[ShawnaB]

You are beginning to see the difference between MASTERY and RECOGNITION. In the pedagogy of teaching, it is understood that there is a vast difference between the two concepts.


Jen

Jen...exactly. This is exactly what I am seeing. Thank you for articulating so well. I also worked this year as a teacher for a charter school, overseeing the personal learning plans of homeschool students. All year, we have been in staff meetings strategizing how to raise students' math test scores on the CAASP test (the adopted Common Core assessment for my state.) There is a lot of talk about "mastery"....but in practice, my colleagues (myself included) mistake recognition for mastery. And what is accepted pedagogy for math instruction does not result in mastery. And the curriculums that public schools provide do not support mastery.

Common core math is highly focused on complex, multi-step problem-solving at a very young age. Students are taught to solve problems in multiple ways, and much time is spent on talking through their thinking. And teachers are trying to do this with students who have to count on fingers to find 8 +6. On the other hand, a student in the 2nd grade who spends all year mastering addition/subtraction facts to 12 and addition and subtraction by carrying is not going to meet the Common Core standards. So I come here seeking encouragement that it is really OK to follow a different path...the path of teaching math that resulted in humans who developed the space program before we had computers!

And then I read this article again for the 900th time and it helps too! -https://www.memoriapress.com/articles/why-johnny-cant-add/

[buckeyelaw]

Thank you so much to the moms who have been through this from beginning to end for sharing your wisdom! I frequently second guess myself when it comes to math curriculum with my 2nd grader (my oldest). He has a natural talent with numbers that I simply do not have, and I worry that I am not giving him the "right" math to help him succeed in what will likely be a science/math career. I feel confident in my choice of curriculum and pedagogy for every other subject, but since math has never been my strongest subject, I do wonder from time to time if I am doing it right, and I begin to research other math options. Thankfully my husband is math-minded, and he helps talk me down off the "should we change to Singapore, etc. etc. etc." so I'm not constantly switching things up on my poor child! My husband agrees with the whole mastery concept, so I continue trucking along with R&S as our spine, and add in RightStart math games for fun game time (well, it's not fun for me, but my son just loves having special time with just me to play these games).

[BearWallowSchool]

Before you advance your student too far ahead know, too, that speed in recall of those facts is important. It is third grade when we begin the written speed drills with 100 facts. The goal for 3rd is 5 minutes, 4th graders have 4 minutes, 5th graders have 3 and 6th graders 2 minutes. We want those facts to be automatic. This can be attained only through consistent daily practice and review.

Something to consider.

Michelle,
Are these drills in addition to the little speed drill booklets that come with each grade? Are the drills found in the blacklines or are you getting them somewhere else?

[enbateau]

For 3rd, the speed drills are in the Blacklines (100 problem pages) and in a small tear-off booklet that has between 28 and 30 problems. In R&S Arithmetic 2, there are workbook pages at the end of most lessons with 28 or so problems timed at 1 minute as well as a grade 1 speed drill booklet with pages of 18 problems.

[Michelle T]

The 100 facts are included in the 3rd grade. There is a speed drill book and the 100 facts drill pages. The regular speed drill is in a little book the 100 facts come in a little packet and are reproducible.