M5U1A3 – Malin Matus – Reflection on Understanding and Applying Standards

Introduction

In this blog I will reflect on what I learned about unpacking educational standards and using backward mapping to plan a unit of study guided by the standard. Personally, I feel that learning to unpack standards and to plan by backward mapping was hugely useful. I think that the unpacking strategy was helpful allowing me to really breakdown what content and skills needed to be taught in a given context. Similarly, I believe backward mapping to be a very important planning strategy for teachers to ensure that their lessons are taking students along the correct path, and to make sure that all of the lesson paths link together to reach an ultimate conceptual destination. For me learning these strategies has been overwhelmingly enlightening and I have mainly positive impressions to share. Never the less, there are one or two pitfalls that come to mind when I think deeply. I will divide my reflection into two main parts, unpacking standards and planning through backward mapping. For each part I will go through examples of the helpful strategies I learned and insights that I gained. I will then finish each part with a brief discussion of any of the weaknesses I felt were inherent in that approach.

Unpacking a Standard

This module of Teach-Now was not the first time I had encountered an educational standard. In fact I have been seeing them in textbooks or on course outlines since I began teaching English in Japan over ten years ago. I mostly used the standards as guidance into content instruction or if I felt they were too boring or unrealistic I’d disregard them. However, in activity one I learned to truly interpret a standard. To give a more concrete example I will look at a simple math standard I used in activity one.

(1) To help pupils understand the meaning of units and measurements of area, and determine the area by calculation.
a. To get to know the units of area (square centimeter [cm2], square meter [m2], square kilometer [km2]).
b. To explore ways to determine the area of squares and rectangles.
(MEXT, 2008, p.12-13)

Before this unit and activity one I would have interpreted this standard to mean, “Teach the students about measuring area of squares and rectangles and be sure to include sizes that use square centimeters, meters and kilometers.” That would have been it and I would be off teaching. Now, however, I look at this differently. I would of course pick out the content words as I did above (measurement of area in squares and rectangles) but I have now learned to analyze the verbs in the standards as skills. The verbs; get to know, explore and understand all inform different types of activity by the students and therefore inform the teacher to use different instructional approaches. An exploration strategy will involve more discussion, more opportunities for failure but also more opportunities for freedom. The stakes will necessarily have to be low to encourage creativity. On the other hand, an activity to show understanding will have the goal of success, failure will be an undesirable outcome and the stakes will be higher. This insight is the power of the unpacking strategy and it has radically changed how I read and interpret educational standards. This method allows a teacher to tease out the underlying big ideas inherent in the standards and also interpret how deeply to delve into the material.

While the strength of the unpacking standards strategy is, its attention to teasing out all the details and meanings of the verbs and nouns written in it, it is also its weakness as such close reading and analysis takes time. That being said I do feel that with practice the process will become quicker. The one other downside to the unpacking strategy is that it is prey to the wording used by the standards author. What I mean is that if the author uses poor word choice the power of this method is lessened.  For example if vague terms like know or see are used frequently the skills to be taught to the students becomes unclear and more open to wide interpretation. Consider the first part of the math standard above rewritten more vaguely. To help pupils see [understand] the meaning of units and measurements of area, and know [determine] the area by calculation. I replace understand with see and determine with know and if we read the standard written this way it is much less clear what skills the students need to acquire. How does a student know the area by calculation? Do they measure, estimate, use a formula, or some other way? Through this example we see that should a standard be poorly written even taking careful attention to unpack it will not necessarily lend the teacher any additional insight as to the direction of instruction.

Planning by Backward Mapping

While unpacking a standard gives us the instructional focus of a standard, planning by backward mapping ensure that we point our instruction in the correct direction to have it link up with the big ideas and concepts later in a student’s education. Let me illustrate with the same mathematical example from above.

(1) To help pupils understand the meaning of units and measurements of area, and determine the area by calculation.
a. To get to know the units of area (square centimeter [cm2], square meter [m2], square kilometer [km2]).
b. To explore ways to determine the area of squares and rectangles.
(MEXT, 2008, p.12-13)

We unpack this standard and summarize the skills and content to be instructed as:

  • Explore: Try various ways to determine the area of squares and rectangles, without any expectation of success.
  • Determine: Precisely calculate the the area of squares and rectangles i.e. length x width
  • Understand: To be able to use the units and measurements of area, cm², m² and km², in the correct manner to calculate the area of squares and triangles.

We also tease out a big mathematical idea from all this, “Some attributes of objects are measurable and can be quantified using unit amounts” (Charles, 2005, p. 20). Having unpacked all this data a teacher could then go plan a unit to include some direct instruction on what is area followed by drills and homework to practice the concept and then be done. And without backward mapping that is what many teachers do. However, having learned backward mapping I now would approach this much differently. If the end goal is the big idea that, we can measure things in math, then for me that really ties into the idea that math applies to the real world things we can see, touch, taste and smell. We need to incorporate this idea into the lesson. It doesn’t matter that these grade 4 students won’t need to know a big math idea like the one above, backward mapping is about ensuring that we point ourselves in that direction at each instructional point. This is so that when the day comes that a student does need to understand the big math ideas around what is measurable in math, they will have had sufficient experience to do so. With this goal in mind I would design activities that touch on the concept of what area is (l x w for rectangles and squares) but I’m also going to include real world stuff. Stuff like taking a meter stick and measuring the area of whatever surfaces we can find. Activities like trying to write your name on graph paper where you have to use the squares like pixels but you can only use a limited area. It is through these activities that the student will begin to develop the schema to understand the big ideas in math associated with the area of objects. This for me is the beauty of backward mapping. Keeping learning aligned along a purpose that serves a long term educational goal and the development of conceptualization in students rather than fact acquisition or skill repetition.

I like backward mapping as an instructional planning strategy a lot and I am hard pressed to think of any negative points about it. The only thing I can think of is that when you are looking at the big ideas all the time to align your lessons and units it could be overwhelming. The big ideas may seem too big, and teachers may question how do I get elements of that advanced concept into a simple context or lesson.

Conclusion

In this blog I shared my experience of learning to unpack standards and to plan instruction by backward mapping. Overall I believe that both are powerful tools for my teacher’s toolbox and I plan to use them extensively for as long as I have to plan and teach. Through unpacking standards I learned how to focus not only on the instructional content of a standard but also the skills for students to learn and demonstrate, as well as, the underlying big ideas included with the content area. Learning about designing instruction using backward mapping helped me understand how to use the large concepts, major skills and big ideas of a content area to align my instruction to continually develop and reinforce transferable skills that will serve students from lesson to lesson, unit to unit, year to year. Altogether learning these two strategies has been an eye opener and very valuable to me as an already practicing teacher and career educator. I wish I had learned these two methods years ago when I first started teaching.

References

Charles, R. I. (2005). Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics. Journal of Mathematics Education Leadership, volume 7, number 3. [PDF file] Retrieved July 13, 2017, from https://www.google.co.jp/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&sqi=2&ved=0ahUKEwjJpLyVu4XVAhViCMAKHWnQAgYQFggkMAA&url=http%3A%2F%2Fwww.authenticeducation.org%2Fbigideas%2Fsample_units%2Fmath_samples%2FBigIdeas_NCSM_Spr05v7.pdf&usg=AFQjCNHKmtdKmLq_V0mw9NIqi0dW3U_zqw&cad=rja

Ministry of Education, Culture, Sports, Science and Technology [MEXT]. (March, 2008). Improvement of Academic Abilities (Courses of Study): Section 3 Arithmatic. [PDF file] Retrieved July 13, 2017, from http://www.mext.go.jp/en/policy/education/elsec/title02/detail02/1373859.htm

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