Wednesday, March 25, 2015

What Makes a Teacher Outstanding?

Tonight I'm asking you to help me write a blog post.  We have all read or heard the research that states that teacher quality is the single most important factor in student success.  Not class size, not resources, not even socioeconomic factors.  Teacher quality.

That has me wondering, how do we define what makes a teacher outstanding?  What are the characteristics that an outstanding teacher possesses?

Here's where your part comes in.  Please think of a teacher you have worked with who you would consider to be truly outstanding and leave a brief comment describing one or two important characteristics that teacher possessed.  You might also think about a teacher that was not outstanding and comment on what they lacked.  I will compile all of your wonderful comments into a future blog post, so PLEASE sound off!!

Sunday, March 15, 2015

What's My Number? Differentiating in K-1


In her book How Children Learn Number Concepts, Kathy Richardson devotes an entire chapter to composing and decomposing numbers.  It may surprise you that the title of the chapter is Understanding Addition and Subtraction: Parts of Numbers.  This quote sums it up beautifully:
"If basic facts are to be foundational, they must be based on an understanding of the composition and decomposition of numbers."
Both the CCSSM and Texas TEKS have a number of standards in Kindergarten and 1st Grade related to composing and decomposing numbers, as shown in this table.

One important feature of the standards that is often overlooked is that they describe the level of concrete or pictorial support a student should receive.  Notice that K.OA.3, for example, states that students should use "objects or drawings" and record the decomposition using a "drawing or equation."  In that one standard, you hear each phase in the concrete, representational, abstract (CRA) sequence of instruction.  Notice how the concrete and pictorial are tied to the abstract (equation) to help students make that important connection.  Rushing students to abstract, or purely symbolic, learning is a recipe for disaster, and that is recognized in the standards.

Composing and decomposing numbers is such a critical component of number sense that it should constitute a a major part of the learning that takes place in Kindergarten and 1st Grade.  Richardson states, "As children learn the combinations that make up the numbers to 10, they will reach the point where they know the parts so well, they can identify a missing part when they know the total and one part."  In other words, students need lots of practice composing numbers, working with the various combinations of each number, before they will be able to decompose numbers, or find a missing part. In your bag of instructional tricks, you will want to have a wide variety of activities to practice composing and decomposing numbers.  These blog posts will give you ideas for activities as well as freebies you can use this week!

  1. Shake and Spill
  2. Mathemagician Make Ten
  3. Make 5 Go Fish
  4. In the Cave
For all of these activities, it's important to understand that students should master the combinations for one number before moving on to the next.  It does no good for a child to practice composing and decomposing 6 if he does not know the combinations for 5. That's where differentiation comes in. Richardson describes using the "hiding assessment" to determine a child's fluency with each number. To determine if a child knows all the combinations for 3, ask the child to count out 3 counters or linking cubes. Hide some counters and show some, asking the student to identify how many are hidden.  For example, hide 1 counter and show 2.  "If I have 3 counters and 2 are showing, how many are hidden?"  Continue this routine for each combination for 3 (hide 3, show 0; hide 2, show 1; hide 0, show 3).  If the student can name all the missing parts for 3, try the combinations for 4.  When the student can no longer easily name the missing parts, that becomes her number. Use a recording sheet to keep track of each student's number so you can differentiate activities, such as those described above, based on each student's needs. For example, all students might be using Shake and Spill in a workstation this week, but each child is using his or her own target number.  Every few weeks, "test" your students to determine if they are ready to move on to a new number.

While it might seem daunting to differentiate based on each student's number, the good news is that a few engaging activities go a long way.  Constantly rotating the activities keeps engagement high and allows you to meet the needs of each student without a great deal of prep work.  For more great activities, check out Building Number Sense: Games and Activities to Practice Combinations for 10 or these other blog posts tagged with the key word "compose."  

Sunday, March 1, 2015

Rebranding "Show Your Work"

Marketers know that a product's brand is everything.  If a product is not selling to its potential, one solution is often to tweak the brand, or "rebrand" the product.  Kentucky Fried Chicken changed their branding to KFC to de-emphasize 'fried chicken" and appear to be a more healthy option.  If it works in business, shouldn't it work in education?

In math classrooms across the world, students are told on a regular basis to "show their work".  I wish I had a nickel for every time those words came out of my mouth during my educational career.  It is certainly done with good intentions--it is critical that students are able to communicate mathematically. Not to mention the valuable feedback teachers receive when they analyze the "work" a student has shown.

My problem is not with the process, it's with the words, so I have been experimenting with rebranding "show your work".

As I see it, there are two major problems with asking students to show their work. First, the words hold a very negative connotation in the minds of students.  It's something they have to do.  Furthermore, the words are often delivered in a way that is not conducive to cooperation.  "John, if I've told you once I've told you a million times, you've GOT to show your work."  "Valerie, I'm not taking this paper until you show your work!"

Second, many students don't show their work because they don't know what the heck it means!  My favorite is the student who circles the multiple choice answer he thinks is correct and then x's out the other choices.  If you ask him, he is "showing his work".

For my suggestions, I will address the second problem first.  Students have to be specifically taught what it means to show mathematical thinking (see how I'm rebranding it?).  This happens through a great deal of modeling and coaching.  I'm blessed to work with small groups exclusively, so I am able to coach my students one-on-one, helping them to understand how to comprehend and make sense of each and every sentence in a math problem.

Now, to overcome the negative connotation of the words "show your work", we have to stop using them.  Think about it, when you are solving a problem do you think to yourself, "Hmmm, I've got to show my work."  I don't think so.  What I DO do, is make notes to myself as I interact with the problem.  Those are now my go-to words when working with the students--I document my mathematical thinking by making notes as I interact with the problem.

I have been using this approach with my students for about a month now, and I am very pleased with the results.  They seem more open to the process and, through coaching, they are learning how to take notes on their own and determine important information.  It's a thinking process, not a rote procedure. In a follow-up blog post, I'll discuss more about how I help them make sense of problems.

I'd love to hear your thoughts!!

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