After completing my reaction paper to the NCTM standards and Common Core Mathematical Practices, I was inspired to change course this week. I wanted to take the math practices out of the abstract investigate ways to incorporate them explicitly in a lesson. I decided to start at the beginning and focus on Math Practice One. As a reminder, MP1 states "Make sense of problems and persevere in solving them."
I found a great video on explicitly teaching Math Practice One to third graders:
After watching this, I decided to make a MP1 worksheet that would give somewhat of a step-by-step guide for students to use while working on a content problem. Here is my first pass:
I would make this a bit prettier and more colorful for my students, but this is basically the format and info I would want it to include. I tried to design this worksheet with the definition given on the Common Core website in mind. Here is the definition and I will highlight the parts I pulled from:
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Reflection
I think this was a good start on exploring how to include a math practice in a lesson. The video I watched made the point that these practices include skills that need to be explicitly taught. My hope is that this worksheet could serve as a graphic organizer to show students how to think through math problems. The inclusion on the worksheet of multiple methods can hopefully signify that 1) there is not ONE right way to get to a solution and 2) trying a method that doesn’t work is very much a part of the process. Going forward I am hoping to continue working on integrating the math practices with the content standards and I would ultimately love to reintroduce my initial inquiry into collaborative learning along with the standards. My plan now is to work on them separately then start bringing them all together slowly. We’ll see if that works!
Keith this is a great math practice to focus on, making sense of problems and persevere in solving them, as a child math was not my favorite subject simply because it did not have that sense of math concepts being all connected and understanding that math build on itself, so to see this MP1 play out in your learning path will be great to watch.
Keith, What a great idea! I would love to see an actual problem you try to work through. I wish we all had classrooms of our own so that these new ideas could just be put to good use. We could just give the students different problems and your worksheet with a few ideas on how to use it and let them go and see how they flourish! Keep up the great work!
For my final post, I wanted to continue studying possible games for the classroom and I found one that could be an incredibly fun and active way to teach subtraction. It’s called Whack-a-Ball and is modeled after the Whack-a-Mole arcade game (where the player tries to hit as many “moles” popping out of their holes as possible). This game actually begins with some arts and crafts work. The base for the game can be created by taking a shoebox and cutting out 10 circles from the top (as if it were a 10 frame). If the students are given a problem of 8–3, they would start by placing 8 balls on their circles and then “whack” down 3 of them. They would count how many are left and write or speak the answer. Here is a picture of the setup: I think this game is great for kindergarten and 1 st graders and can probably be modified to meet the needs of 2 nd graders as well. To raise this to a high-level math activity I would ask the students to verbally explain h...
Based on our async work this week, I decided to focus on division. I, personally, was having a difficult time identifying the difference between the partitive and quotitive approaches to division. So today I reconstructed two Khan Academy visuals using arrays. Standard: - CCSS.MATH.CONTENT.3.OA.A.2 I nterpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. Partitive: Quotitive: Reflection: Even as I was constructing these arrays, I had a few issues. Specifically, when I was trying to verbalize the partitive approach, I stumbled on wording multiple times. And then it hit me: I have always instinctively approached ...
In response to last week’s presentations on concept games and this week’s reading on technology in the classroom, I’ve been inspired to dive further into two different computer games and investigate their usefulness. I recognize I devalue computer games a bit based on my preconceptions of what “real math” is. That definitely comes from what was available when I learned math (and how it was taught). This week I am trying to break out of that and reorganize my thinking. Game: Alien Addition (Math Playground) This game mirrors space invaders. The student is defending against an alien invasion and must shoot a laser at the spaceship that is labelled with the addition problem that adds up to the number given on the bottom of the screen. This game would help a tremendous amount with fluency. Content Standard: CCSS.MATH.CONTENT.2.OA.B.2 Fluently add and subtract within 20 using mental strategies. 2 By end of Grade 2, know from memory all sums of two one-digit numbers. Math...
Keith this is a great math practice to focus on, making sense of problems and persevere in solving them, as a child math was not my favorite subject simply because it did not have that sense of math concepts being all connected and understanding that math build on itself, so to see this MP1 play out in your learning path will be great to watch.
ReplyDeleteKeith, What a great idea! I would love to see an actual problem you try to work through. I wish we all had classrooms of our own so that these new ideas could just be put to good use. We could just give the students different problems and your worksheet with a few ideas on how to use it and let them go and see how they flourish! Keep up the great work!
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