Category Archives: TK-5 Math

Can we be more deliberate in providing access to the SMPs?

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Yes we can! We can plan our lessons starting with the Standards for Math Practice and focus on student sense-making.

I have been pondering this idea for a long time as I am sure many math teachers do from time to time. How can we focus on the SMPs as drivers of our instruction? How do we incorporate them in meaningful ways?

The reality is that the SMPs are rarely the focus of math instruction, they are embedded in textbooks in superficial ways, and they are difficult to quantitatively assess. The SMPS are listed below and there are great grade level explanations of each SMP in the current CA Math Framework (2013).

I argue that in order to create a more creative and critically thinking society we have a responsibility to focus on the SMPs in our math lessons. Remember, these are the habits of mind that we want to impart on all students. Focusing primarily on the computational/procedural side of mathematics with NOT get us to the reasoning, communicating, and curiosity our students need to solve current and future global problems.

So how could we do this:

  1. Start with identifying a focal SMP for a lesson or series of lessons
  2. Anticipate student successes and struggles
  3. Script possible facilitating questions that align with the SMP prior the lesson
  4. Jump in, reflect, and refine future lessons

Here is an example from 3rd or 6th grade multiplication:
I often think of area models as an example. If you consider lessons around introducing 3rd graders to multiplication through area models you could focus on SMP 4 – Model with mathematics or SMP 3 – Constructing viable arguments.

Depending on which of these SMPs you are focusing on will change the questions and structure of the same lesson.

  • If you focus on SMP 4 – Model with mathematics … then sequencing student work so that students see both horizontal and vertical models or using a routine such as Connecting Representations
  • If you focus on SMP 3 – Constructing Viable Arguments … then the mathematics could easily be embedded in a contextual problem. The 3-Reads or Decide and Defend routines could be utilized and students are given time to solve using their own method. Following that the teacher would ask student to justify their and their classmates’ reasoning.

As an alternative and a parallel to these ideas I also offer this reminder from Dan Meyer’s TED Talk from 2010.

Shifting instruction at all grade levels towards facilitation and away from lecture is essential in preparing our students for their limitless future. There are many ways to achieve this and I offer this post as a way to reach this end.

Math Facts (+, – , x, /) – How do we achieve automaticity? Or is the Question – Do we need to?

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The short answer is through varied practice over several years and to recognize that this is a multi-faceted issue. We have to begin to acknowledge that this issue likely has more to do with student dispositions towards math, which our system perpetuates and creates, than with the students themselves.

The longer answer begs us to have a lengthy discussion about whether or not the need for this learning is outdated. In December I had the great opportunity to work with several groups of teachers and like many other 4th-8th grade teachers they were asking how they can help student learn their math facts.

I do believe in our current system that knowing basic math facts to automaticity makes learning other mathematics easier. Knowing facts means they know from memory or have efficient (for them) strategies to derive the facts they don’t know from memory.

That being said, NOT knowing these facts should never mean a student is denied access to grade level content. Give them a calculator.

I also recognize that much of what our students need math facts for in grades 4-12 are calculations that can be done more effectively with a calculator, computer, google, Wolfram Alpha, and/or PhotoMath, etc. I am often reminded of something Jo Boaler says, “We have to start teaching math as if computers exist.” Said another way by Conrad Wolfram, “Stop teaching calculations, and start teaching maths.”

With all of that comes the need to address our teachers concerns in the here and now. While working with teachers recently we discussed several issues that cause our conception of students lack of facts. There are many things to consider…

First, students know more facts than they realize and often they can’t remember because of other cognitive processes and short term memory that is being used for other things such as dealing with trauma and mindsets around mathematics.

For example, think of a time when you used to know a great deal about something that you no longer remember as well. For example, there was a point in my career when I sold real estate on the side of teaching. Mostly, short sales after the 2007-08 crash, trying to help people navigate the banks. I knew a lot about that process and I remember almost none of it now because I haven’t used the information for so long that my brain naturally made those pathways less defined. We all have learning like this. We have all forgotten things we used to know.

We have to recognize that students likely have the same challenge with math facts. If they haven’t ever created strong pathways or if there are pathways they haven’t used in awhile then this could seem like a lack of knowledge when really they just need a bit of a refresher in a safe, nurturing environment.

Although this is not an exhaustive list of the multiple facets of this conversation, there is one last thing to consider. Practice with facts should occur at multiple grade levels. 6th-8th grade teachers, stop being frustrated and simply provide opportunities to practice as a refresher of skills. This practice should never be timed or any version of forced competition. It should also be varied. Give students choice!

If you truly want to build automaticity, fluency, and flexibility simultaneously in students around math facts, you should look to Number Strings. There are great resources out there for number strings including Context for Learning Units by Cathy Fosnot and New Perspectives on Learning, Pam Harris @ MathisFigureoutable.com, and Teacher Education by Design.

There are great ways to give students practice with these skills (that aren’t BASIC for many students). Use fluency games (www.mathforlove.com), math running records that help students see which facts they know and which they need to learn, online games (many are free), and playing card or dice games that provide variety and engagement. Again, let students CHOOSE how they practice.

Many districts make the erroneous decision to purchase programs TK-5 or TK-8 such as Reflex Math, Dreambox, or iReady and then require ALL students to commit 30-45 minutes a week of class time to these programs because that is what the programs data shows will work. Here is the kicker, if a kid doesn’t like the program at that moment then you are wasting your time. You will never automatize something through forced practice. If you have students that don’t like it, let them practice another way. Have options for them.

This simple idea is the essence of UDL and creating nurturing environments in which students voice is considered in their learning.

There is still a larger conversation to be had about the outdated nature of standards that require this learning. This conversation should include the need to truly move towards mathematical understanding of how operations behave rather than the eventual algorithms that are the unfortunate end result of a great progression of standards in TK-6.

Is there a place for competition in TK-5 classrooms?

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The short answer is ONLY if students choose to compete. This should always be 100% their choice.

Collaboration promotes more learning than competition. This is true for students and adults. The reality is that there are many instances of competition that are implied throughout our classrooms systems in TK-5 education and beyond. For my purposes today we will focus on our youngest learners in grades TK-5. We have to remember that while many of our students like school for a variety of reasons they are still required to be there. If we require them to compete with one another overtly or otherwise we run the significant risk of diminishing their agency, the belief in themselves as mathematicians, and their love for learning. I don’t believe there is a single teacher whose goal it is to do this. We all want our students to thrive in our classrooms.

If we truly want our students to thrive we have to regularly reflect on how our chosen practices effect our students. We should pay particular attention to how our practices effect the least vocal, marginalized, and average students. Often times we hold up certain practices because we focus on the excitement of a few kids while not recognizing the reticence of many in the classroom. Continuous reflection and curiosity is essential as an educator.

A great example of this are the charts we see in many elementary classrooms that track progress for such things as math facts acquisition, number of books read, or other whole class record keeping that is public. These charts are a form of passive competition and the students are not getting to choose whether or not they compete. Imagine how the 5 students with the least stars/stickers on the chart feel looking at this public display of their performance. Does it inspire them to work harder or does it seem like a reinforcement of their public or self-perceived lack of ability? I would argue it is the latter. These charts should never be public. Take them down. They are not having the effect for our most struggling students that you would hope.

Timed math fact tests are another example. The general consensus among math educators is that these tests that hopefully WERE so prevalent in our classrooms a decade or more ago are bad for student motivation, create math anxiety, and do not provide us the insight into student learning that we think they do. But is there possibly a place for these tests. I might argue yes. If students are only competing against their own best times, if it is never whole class or required, and if students get to choose when and if they compete. This could be a “may do” for some students who express a desire. There are some students that enjoy pushing themselves in this way but they should be the one choosing to participate. The key is to be flexible within your classroom, be curious about your students and what they like and don’t like, and offer them choice.

Remember as adults we get choose if we compete, with the exception of public displays of state test data. Do any of us like it when this happens? As an example, we aren’t all required to play on an adult league sports team regardless of interest or ability. That would be insane. Competition is fun when we participate because we choose to compete. Let students choose! Reflect on your practices this summer and how you can utilize competition in your classroom for those who want to compete and eliminate it for those that don’t. It should be 100% student choice on a day to day basis.

Have a great summer! Keep being curious and keep learning!