How much instructional time for math?

How much time is “required” for mathematics instruction?  This is probably the question that I get the most.  It is also the topic or question that I have the least amount of resources or research to support.  However, I think there is a common ground that most would agree makes sense. The first one being that without quantity, it is hard to have the quality mathematics instruction that we know is required for all of our students.  The second is that quantity does not ensure quality.  The third, we will get to in a moment.

Screen Shot 2019-09-09 at 1.23.18 PMFirst, let’s jump in. In Iowa, there is not a “required” amount of time. So, we provide what we have as a suggestion.  This is from the publication Adding It Up from the National Research Council 2001. This is a free download from the link above and this is the suggested citation: Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press. https://doi.org/10.17226/9822,

In Chapter 11: Conclusions and Recommendations, Section: Giving Time to Instruction it says,

“Giving Time to Instruction

Research indicates that a key requirement for developing proficiency is the opportunity to learn. In many U.S. elementary and middle school classrooms, students are not engaged in sustained study of mathematics. On some days in some classes they are spending little or no time at all on the subject. Mathematical proficiency as we have defined it cannot be developed unless regular time (say, one hour each school day) is allocated to and used for mathematics instruction in every grade of elementary and middle school. Further, we believe the strands of proficiency will not develop in a coordinated fashion unless continual attention is given to every strand. The following recommendation expresses our concern that mathematics be given its rightful place in the curriculum:

Mathematical proficiency as we have defined it cannot be developed unless regular time is allocated to and used for mathematics instruction in every grade of elementary and middle school.

  • Substantial time should be devoted to mathematics instruction each school day, with enough time devoted to each unit and topic to enable students to develop understanding of the concepts and procedures involved. Time should be apportioned so that all strands of mathematical proficiency together receive adequate attention.”

Some will argue with “regular time (say, one hour each school day),” and claim there is no evidence.  I think we can all agree that “substantial” time is needed.

60 min

What does this mean? Substantial means “of considerable importance, size, or worth.” I tend to think of the amount needed to “reasonably get the job done.” I know some will say, well then it can be as little as 30 minutes.  I don’t know if that would pass the considerable importance, size, or worth test.  I have others ask, “can it be less than 60 minutes?” I think the answer is it depends.  It depends on so many factors which is why there isn’t research that makes this topic clear.

So, the third common ground point is we have to make a decision that make sense based on what students need and not for the convenience of schedules and systems.

Option one: follow what the recommendation has been for almost three decades, which is 60 minutes.

Option two: go with local data and evidence. What does your data say? What do the teachers say? What does the evidence say?

Please let me know what you think in the comments below and what is working, is it 30, 45, 60 minutes or more?

What is CBMS and why should we care?

It recently occurred to me I have been chasing my tail and did not realize it?Screen Shot 2019-06-30 at 12.16.04 PM.png 

While talking to some educators the other day, I found myself intrigued how differently we were describing and framing a topic.

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I thought to myself, “if only we had a unifying network to help understand better. Like a mathematics and mathematics educator network.” Then I had a “seriously” moment. A moment when I say “self, how did you not “get” that before, seriously?”

We do have a network of mathematics and mathematics educator. I realized that it has been right in front of my face the whole time.

This network of professional mathematics organizations is known as the Council Board of Mathematical Sciences or (CBMS). It is the “umbrella” organization that connects all of the other formal mathematics groups.  I like to think of it as our “math solar system,” with “math planets.” These 18 organizations or planets if you will, offer a network and access to the best of the best.  Each planet has a national president and some even have regional or state affiliates like National Council of Teachers of Mathematics (NCTM) and National Council of Supervisors of Mathematics (NCSM).

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I realize now that this is our collective efficacy, which has an effect size of 1.57 according to John Hattie.  I also realized that I (we) collectively are underutilizing this vast resource. I can tell from only scratching the surface of only a few of these planets, most of what I have needed and others have needed (if not all) is from one these planets. This is what caused me to say, “self, seriously?”  The hours of time I have wasted going down “rabbit holes,” “google holes,” and “e-mail holes” when what I needed was in front of me the whole time.

Now, I have made the commitment, that before I look outside of the mathematics solar system, I am going to make sure, the resource, information, knowledge, research, position statement, white paper, practice, strategies, tool, etc. is not on one of our math planets.  Here are the 18 professional organization or planets.

As I previously stated, I have just begun to scratch the surface of the vast resources that this mathematics “universe,” network, community has to offer. I wish when I would have realized this three years ago and even longer ago when I was just a teacher. I hope that through this sharing of this realization, it will encourage educators who are seeking for mathematics “best” practices to look at the 18 planets to find the tools you need.  My call to action is for you to pick a planet and explore. You will be surprised by what you find.

 

Why do you keep saying Number Sense?

Whenever someone asks me how to impact mathematics instruction, I say Number Sense. Yet, some may not be truly sure what I am referring to.  Is she talking about a program, standards, pedagogy, professional development?  What I am talking about is plugging the hole with a finger.

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In the “The Boy Who Saved the Netherlands,” the lockkeeper’s son saved the town by placing his finger in a leak in the dike when the hole was small.

That is what I mean when I say Number Sense. I am talking about plugging the hole when then hole is small.  In K – 2nd grade, the hole is smaller than it will ever be for a student.  That is when we need to “plug it.”  This is the moment to make a difference.  Can we do it later, sure… but understand the hole will be bigger. It will take more fingers.  If we want to plug the hole when it is small, then Number Sense is how we do it.

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So, what is this Number Sense I am talking about?  First, it is helping teachers to develop it for themselves.  Number Sense is a thing that if I as an educator do not possess it, then I cannot help students to have it.  I know this because I did NOT have Number Sense as a secondary math teacher. I had no Number Sense.  I, as a math educator (ALL levels), have to have it so I can make good instructional decisions for students so they can develop it.  It is about giving them experiences that allows their brains to grow and to develop it.  It is not a worksheet or a computer program.

It is how do I make sense of quantity in the context of the world around me.  It is can I look at 3 fingers and know that is 3 without counting?  You just tried it. Now, try it again. Yep, still 3.  Now, what about 5?  Did you know 5? How?  What about 3 fingers and 4 fingers?  What is the maximum number of things that you know the quantity of without counting?

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So that is step one of Number Sense and some of our students cannot do that.  That is when the hole is small.  They just didn’t get as many of the experiences they needed to have their brain grow and develop that.  But the good news is that it is not too late.  This can be developed at any time and any age.

The truth is, if students cannot know how many of something is without counting, then it is really, really hard for them to know 5 and 10.  If they do not know 5 and 10, then they will not understand our number system which is base 10, based on 10.  Which means it is almost impossible for them to know part-part whole which is foundational for fractions and algebra.  There it is!

Why can’t our students do algebra, because they have no Number Sense.  Algebra is not the gatekeeper for college and career readiness, Number Sense is.  If I cannot see quantity, then how can I see “structure,” which is what algebra is, representing quantity abstractly.  Then if I cannot see structure, then I cannot see space – Geometry.   Number Sense is what is limiting access to algebra.

This is why I keep saying Number Sense. I want us to plug the whole when the hole is the smallest.

IM Resource: What’s the difference?

Illustrative Mathematics (IM) recently announced a few more partnerships which has left some educators wondering, who, what, when, why, huh?  Users are now faced with choices and it can be confusing. This post is to help so educators can go back to what is important, focusing on all students having access to aligned instruction in mathematics.

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If you are using IM resources then it is probably because of the review in EdReports.  The IM resources has the highest rating on Ed Reports for the Shifts: Focus, Coherence and Rigor. It is also rated high for usability.  In addition, it contains instructional practices that are held near and dear to mathematics educators.

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But, one shoe does not fit all!   We want options and lots of them. Consider something as simple as buying acetaminophen or Tylenol.  We have rapid release, PM, enteric coated, extra strength, 24, 50, 100 count, tablets, capsules, etc., you name it.  Some people are okay to take the generic and some want the brand name.

The same way with a highly-rated aligned resource.  There are options. Plain and simple, options.  Users can decide what is important to them and what version they will use.  Each will have strengths and challenges.  It is up to educators to pick which option is best for them.  Some will use exclusively from one partner while some will use different parts from several.

In Iowa, we know alignment to the Shifts matters. We know Focus, Coherence, and Rigor matters. This means EdReports can provide useful information when considering which resource to use.  Since the IM resources are highly aligned, then it is important we use a “certified” version. Yes, it matters.

If you have ever talked to me about making changes to the IM resources, then you know I make no bones about owning the fact that, “I do not have the skill-set to know how changes to the resource will impact the alignment and I cannot tell you how it will/will not impact the scope and sequence. ”

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I am not embarrassed to admit it and do not think I should know. What I do know is students deserve the best we can give them and aligned materials matter.  Hard Stop! Students deserve resources which are aligned to the Shifts: Focus, Coherence, and Rigor, and instructional practices. Teachers deserve to teach with highly aligned instructional materials.

So, whether you use the free version or want the additional bells and whistles that come along with the paid version, students and teachers deserve the guarantee that the version they are using is the genuine, authentic, original, “certified” resource. They deserve to know the review from EdReport is intact. They deserve the assurance that any changes made will not alter the scope and sequence or hinder the Shifts. They deserve the changes to be “certified” by IM.

Having access to aligned mathematics instruction should be a right and guarantee each and every student is given. IM is committed to this promise and is providing a guarantee that with the “certified” versions, any changes will not hinder this right and guarantee. This is a very exciting time as the narrative has changed to which “certified” version of a highly aligned instructional resource should we use. It is a good problem to have.