2nd Grade Math

miss-m

miss-m

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Hey all!
I have a question about 2nd grade math standards. I was talking to a coworker who mentioned that she knows someone who teaches abroad, and their math is really just three primary skills for each grade level that are taught exclusively until mastery. Then the next year, they don't have to review and keep practicing; they already know it.

So I'm curious if there would be a way to implement something similar with CCSS. I really only know 2nd grade and that's what I will hopefully be teaching next year, hence the title.

2nd Grade math covers a LOT - addition facts, basic subtraction, counting and skip counting within 1000 by 2s, 5s, and 10s, identifying and categorizing basic 2D and 3D shapes, collecting data, simple fractions (1/2, 1/3, and 1/4), and working with place value up to hundreds. This is by no means an exhaustive list, but these are the main overarching skills taught in 2nd grade, as the addition and subtraction ones also have standards involving solving word problems with one or more steps.

My question is: if you were to put those into groups to really keep instruction focused to 3 or 4 main skills, how would that look? Is this even possible with common core? I like the focus that CC has on critical thinking skills, but what I've noticed is that it is a lot to learn in almost too short a time to really attain mastery of any particular standard.
 
I'd be very careful about your co-workers explanation about what is done in other countries without seeing the standards and curriculum.

For example, teaching students to add can include fractions, positive and negative integers, decimals, etc. It may not be as simple as adding positive integers.

I absolutely do believe spiraling fails many students because it touches on something and moves on, but as I said, I'd be very careful thinking that they teach 3 standards and compare them to what we think of a standard.
 
a2z said:
I'd be very careful about your co-workers explanation about what is done in other countries without seeing the standards and curriculum.

For example, teaching students to add can include fractions, positive and negative integers, decimals, etc. It may not be as simple as adding positive integers.

I absolutely do believe spiraling fails many students because it touches on something and moves on, but as I said, I'd be very careful thinking that they teach 3 standards and compare them to what we think of a standard.
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Of course! That's why I used the word "skills" instead of "standards" in my description of what my coworker said (which could be half-forgotten by me, in all honesty). That's why standards are broken up into classifications - operations and algebraic thinking, geometry, measurement and data, and numbers and operations in base ten (for just 2nd grade). But it's been a thought I've been processing for a week or so now, so I figured I'd get other teachers' input.

I guess my question is whether it would be beneficial for students to teach those skills as a set rather than as spiraling/individual standards, or if that's basically impossible given the way the standards are set up here. For example, is there any benefit to clumping the skills addressed in the four OA standards (Representing addition and subtraction problems, adding and subtracting within 20, and working with groups of objects to develop foundations for multiplication) to one overarching skill taught to mastery?
 
Leaborb192 said:
I doubt very much that we could do something like that unless we seriously scaled back the standards or gave more time to learn them which would push the school year way beyond the 180 days. I would say that as a classroom teacher YOU could create target or "Power Standards'' for each quarter and teach /re-teach to ensure that the students have mastered what you (and your team) deem to important. You could sit down and say "what do our second graders going into third grade absolutely HAVE to know'' and put a lot of time into it so that you can send them on knowing that 100% of them have mastered the standards, which will help with review in the next grade as the teachers won't have to spend as much time on it. This, of course, will help because they can jump into their own standards quicker.
:)
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This is what I was thinking - 2nd grade would actually be easy because there are only 4 categories of standards for 2nd grade (OA, NBT, G, and MD) and it would be fairly simple to do one per quarter exclusively, or work on the largest one (which I think is NBT) to mastery before teaching the others.
I just don't know if that would actually be beneficial to students other than the fact that I'd be teaching to mastery rather than, "Well, some of you have it, and if you don't, oh well, we'll come back to it later (maybe)."
 
I didn't express myself well. I apologize. I would want to see what they do and what it encompasses before I made a judgement about whether or not it is better.
 
Excellent question! IMO, many teachers fail to teach to mastery primarily due to poor student engagement and/or insufficient practice. I seriously doubt if any teacher in the world can get away with teaching just three primary skills for each level - third-hand accounts often exclude key information. A closer examination would probably show that multiple standards are addressed via highly-integrated lessons. Instead of teaching a million individual skills in isolation, skilled teachers are able to design their integrated lessons so that students learn and practice new skills along with those that have already been learned - a developmental learning curve is followed to further optimize instruction. It is the continuous exposure and practice to groups of related standards that facilitate teaching to mastery.

For example, when teaching basic addition facts why not begin by presenting students with Unifix cubes that are in groups of 2s. Show them that two groups have four cubes, three groups have six cubes, etc. Only after they have mastered this "skill" should they be introduced to adding groups of 3s. As you can see, students are simultaneously exposed to both addition and multiplication concepts in this activity (even though multiplication is not a second-grade standard!). This is how accelerated instruction can be achieved. Although this example may seem like an oversimplification of the process, it hopefully shows how one can keep up with the pacing guide and still teach to mastery.

Where does your coworker's friend teach school?
 
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As a former special education teacher, I should mention that it often helps to minimize confusion when new concepts are introduce by refraining from using too much academic jargon. You might consider postponing the use of words like equals, times, etc. Instead of equals use "makes" and instead of times just say "three groups of twos". Also use only one color of Unifix cubes.
 
I doubt it.

While there are relatively stand-alone concepts, and you could arguably group some into earlier years and others into later years, many of the concepts are interconnected (see: https://achievethecore.org/coherence-map/ -- it maps out every CC math standard and what else it connects to) and students are not necessarily developmentally ready to fully grasp the meaning of some concepts at the time, and need it to spiral back around when their brains have developed more.

What I'd like to see more is less of a formulaic, follow-the-curriculum style where each day is a different learning target and starts with a lesson, and ends with practice...and find ways to incorporate more exploration and integration of multiple topics.

There's a great Week of Inspirational Math activity that I did with my kids (4th) that had them looking at shapes, multiples, factors, multiplication, patterns, prime/composite, at a minimum...all in one activity they did over the course of about an hour. I realized today that, while
 
My opinion is that our curriculum is about a mile wide and an inch deep. Yes, that's a generalization and implementation differs widely. Because of the breadth and lack of depth, I think we leave far too many kids behind. That said, I tutor a 3rd grader, and was going to start working on fractions with her (I'm not privy to her classroom plans) and she easily colored in equivalent fractions. Then she surprised me by showing me that she knew how to use cross-multiplication to demonstrate equivalency. That is just one child, though, and she seems to have above-average skills.
 
Upsadaisy said:
Then she surprised me by showing me that she knew how to use cross-multiplication to demonstrate equivalency.
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A deeper question: did she understand what was happening with the cross-multiplication, or was it simply a "I know how to follow this procedure"? For example:

I think part of the breadth and lack of depth speaks to teacher comfort, especially when going beyond just the teaching of the initial skill (i.e. the depth of understanding, the meaning behind procedures, etc...). As I've mentioned to many people - my "eled math" courses in my teacher program were incredibly scary...incredibly...

I feel that if there was greater emphasis on that depth from the get-go, while there might be fewer students that'll go far "beyond grade level" - only in the sense of learning more and more procedures and "tricks" - it'll bring up those who are struggling and strength the core of those who would usually excel, but only with a weak core foundational understanding of what they're doing.
 
Let's face it, we've all known teachers who skipped all the word problems in their lessons because they, themselves, weren't comfortable with them. And the advantage of advancing 'beyond grade level' is one which doesn't really mean much until later years of school, although it is wonderful to see kids with natural number sense and math aptitude.
 
Personally, I prefer to teach math with the skills/standards merged together. It makes planning the math lessons a lot easier.
Now, creating workbooks for each strand....
I have seen this done before and it usually works.
Both options will require intervention, remediation, practice, and hands-on activities/interactive projects.
 
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