As a teacher I believe that it is paramount that we use standards to guide our teaching, or learning opportunities. Standards are the sign posts by which we guide our methods and thus our students learning to a goal. Alignment through the grade levels within a school without the use of standards would be an almost unachievable task. Imagine if I was, as a 3rd grade teacher, preparing to teach a math unit on multiplication to only find out during my first lesson that the students did not know the beginning of their times tables? Having standards and using them to guide every learning opportunity would eradicate this problem. The above graphic is a standard for a Math unit that I unpacked bu using a technique explained in the book by Hubbell & Goodwin, B. (2013), The 12 Touchstones of Good Teaching: A Checklist for Staying Focused Every Day. Below is the explanation of that unpacking and hopefully it can help other's to successfully unpack their standards as well.
I chose to unpack the standards by determining the declarative and procedural knowledge that students would need in order to master the standard and then using the determined vocabulary to conduct the unpacking (Goodwin & Hubbell, 2013). Within my unpacked standard I included a bullet point that says I will be using a visual representation model to help teach the standard. This type of visual representation is supported by several sources, but the source that I chose to support is that of Berdynaj and Vula (2011). The current visual representation of multiplication, division, addition, and subtraction that is being used in my classroom is the ‘bar model’.
I find this type of visual representation to be quite effective when realia are not present in the lesson to reinforce student understanding of the concept. These bar models can. As stated previously, be used to teach multiplication, division, addition, and subtraction. To address struggling or remedial students I will employ physical counting blocks and baskets to demonstrate how division or multiplication can work in real world situations. A remedial activity would take the form of have a student sort twenty 1’s place math building blocks into 4 equal piles while having the student count the number of blocks they can put in each pile until their original 20 is depleted. The number from each pile would be the visual representation of 20 ÷ 4. The same process can be done in reverse for multiplication.
For the next bullet point of ‘Students will need to be able to carry and regroup numbers in multiplication problems’ a good bit of pre-learning and mastery will have taken place in previous units. However, when moving into multiplication that will be using the hundreds and thousands place it will be paramount to reinforce that you can regroup, or carry, the tens place into the hundreds place. I will be doing this with the following graphic used several times with several different problems in the explicit teaching model of ‘I do, We do, You do’. For a remedial student I would use the same method as mentioned above with having physical manipulatives to reinforce the process. See figure 2 for an example of regrouping into the hundreds place.
The final bullet point of my unpacked standard I expect to take at least 3 lessons in itself to fully relay to my students. I imagine I will be using the following graphics and a synthesis of old-fashioned white board writing in conjunction the explicit teaching model that I use for all of my math lessons. Before even showing a graphic explanation, I would have the students solve these 3 short division problems: 4 ÷ 3, 12 ÷ 3, and 6 ÷ 3. I would then write the long division problem of 426 ÷ 3 and relate to them how the way of solving this problem is just the same as how they solved the 3 ‘easier’ problems. I think this approach will also work with remedial students, if not then I will change my tactic.
Hinton, V., Stroizer, S., & Flores, M. (2015). A Case Study in Using Explicit Instruction to Teach Young Children Counting Skills. Investigations in Mathematics Learning, 8(2), 37–54. doi: 10.1080/24727466.2015.11790350
Hubbell, E. R., & Goodwin, B. (2013). The 12 Touchstones of Good Teaching: A Checklist for Staying Focused Every Day. ASCD.
Lirika Berdynaj, and Eda Vula. “Collaborative Action Research: Teaching of Multiplication and Division in the Second Grade of Primary School.” Turkish Online Journal of Qualitative Inquiry 2.2 (2011): 7–16. Web.
(Singapore), S. E. I. (2014). PR1ME mathematics 3A Teachers Guide. Singapore: Scholastic Education International (Singapore) Private Limited.
Benjamin Snitker. A master's candidate at Colorado State University-Global Campus.