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Thursday, May 31, 2012

Foundations Series: What is Dimensions? - Topical/Conceptual Knowledge

Greetings alignment fans! I hope that all of you had a fantastic Memorial Day Weekend, and are feeling rejuvenated. I know I am. I spent the weekend with my wife and dog in Fargo, ND visiting some dear friends. Believe it or not, I didn't even think about alignment. Ok, I hardly thought about alignment. Sometimes it just jumps right in ol' noggin. So, last month, I more or less took off from blogging. Nevertheless, I'm here to dig into another foundational alignment concept. Before I get too far down that path, let's briefly recall the working definition for the term alignment:

"the extent to and how well all curricular categories and the elements within them (e.g., content standards, instructional content, and assessment practices) work together to guide instruction and, ultimately, facilitate and facilitate student learning." (e.g., Webb, 1997)

The point of this definition isn't just that alignment means that curriculum is coordinated/similar. The bigger point is that this coordination is done for the purpose of supporting student learning. If that's not our clear purpose, then our work is misguided. Ok, moving along...

The month before my brief hiatus was focused on the question "What is Directionality?" You can see the overall alignment picture for the framework I use, as well as where Directionality fits, under the green oval on the left.

This month, I will focus on the question "What is Dimensions?" You can find that in the figure above under the blue oval in the center. That question, I realize, is a bit clunky the way it is phrased. Think of it this way: the term Dimensions is a categorical label. Anyway, Dimensions is such a broad and important concept, I'm actually going to be breaking it down into three sub-categories, each of which I will explore in single blog posts. I will start with the alignment dimension of Topical/Conceptual Knowledge.

What is topical/conceptual knowledge? 

Briefly, topical/conceptual knowledge is:

the subjects, information, and ideas that students are supposed to learn. (Niebling, Roach, Rahn-Blakeslee, 2008)

A less elegant way to state that definition is this: stuff kids need to learn. Through this lens, we aren't concerned about what students are supposed to do with the "stuff" they are learning, what sort of cognitive activity we hope to evoke in their minds. No, this is really just about the facts, topics, ideas, and concepts they are supposed to learn. Here are some examples:

  • math facts
  • the Civil War
  • photosynthesis
  • author's voice
That's pretty straightforward, right? As stated, the above examples are just topics or ideas. Let's ratchet this up a notch, shall we? Let's look at some Common Core standards and see if we can pick out the topical/conceptual knowledge in them. I'll provide on English/Language Arts example and on Mathematics example. Here we go...

English/Language Arts
Standard RI.5.3. Explain the relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text based on specific information in the text. 

What is/are the topical/conceptual knowledge of this standard? Think for a minute. Then scroll down and see what I think. :)

Got your answer? Here's what I thought. I believe the topical/conceptual knowledge in this standard can be found in this portion of the standard: "relationships or interactions between two or more individuals, events, ideas, or concepts in a historical, scientific, or technical text...". The standard calls on students to learn about relationships or interactions that are detailed or described in different kinds of texts. Do you agree or disagree?


Now, let's try a math standard:

Standard 3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters.

Ok, same as before. What is/are the topical/conceptual knowledge of this standard? Think for a minute. Then scroll down and see what I think.

Got your answer? Here's what I thought. Here are the parts of the standard statement that I thought contained the topical/conceptual knowledge of the standard: "measurement data...halves and fourths of an inch...line plot...horizontal scale...appropriate units—whole numbers, halves, or quarters." In my opinion, this one wasn't quite as neat and clean as the ELA example. But I believe you can see several concepts described in the standard. There are a variety of types of measurement data (e.g., temperature, length, weight, etc.), each of which can be broken down into different units. Data can also be displayed in a variety of ways (e.g., line plot, bar graph, pie chart, etc.), again broken down into different units.

In each of these examples, we've isolated the topical/conceptual knowledge called for by the standard, but we haven't gotten into what students are supposed to be able to do with that topical/conceptual knowledge. That is critically important, but I will save that issue for next month :).

What does research say about topical/conceptual knowledge?

Sadly, we know little from research about topical/conceptual knowledge. Candidly, most research on opportunity to learn and alignment does not break down Dimensions into different categories. There really isn't any acknowledgement that Dimensions is a "thing." In my opinion, we can look to two general areas of research that can shed a little light on the subject. One area is descriptive, the other predictive.

Descriptive research

When it comes to descriptive research, we can look to work done to describe the degree of alignment between two curricular elements (e.g., intended, enacted, assessed, learned curricula). Norman Webb's (e.g., 1997) work on alignment does examine what I would consider to be a form of topical/conceptual knowledge. I would say his version of this concept is what he calls categorical concurrence. Basically, there is a high degree of categorical concurrence across standards and assessments if the same or consistent categories of content appear in both the assessment and the standards.

Andy Porter and his colleagues (e.g., Porter, 2002) have created a multi-dimensional alignment framework known as the Surveys of Enacted Curriculum (SEC). Part of the SEC framework includes a set of topical descriptors that relates quite closely to the concept of topical/conceptual knowledge. Examples of these topical descriptors includes "Linear equations" and "Main idea(s), key concepts."

Predictive research

Unfortunately, we know even less about the predictive nature of topical/conceptual knowledge than we do about it's descriptive potential. Put another way, just looking at topical/conceptual alignment hasn't been specifically explored much in research. Perhaps the most telling piece of research comes from Gamoran and his colleagues (1997) who found that just looking at topical/conceptual knowledge alignment didn't predict how well students would perform on assessments. Only when cognitive complexity was added to the analysis could those types of predictions be accurately made. We'll revisit the cognitive complexity issue next month.

What are the practical implications?

In my opinion, the practical implications boil down to a few simple ideas.

  1. It can be helpful to just think about topical/conceptual knowledge alignment first before getting into cognitive complexity. I can't provide you with empirical support for that opinion. It's based on my conversations and work with teachers and administrators who consistently tell me that thinking about cognitive complexity is harder. 
  2. Most work done under the title of "alignment" really only looks at topical/conceptual knowledge, and typically at a coarse-grained level (more to come in future blogs on this concept). Which is a decent-enough place to start, but limited. 
  3. The work gets more interesting (and challenging) when we start looking at cognitive complexity in addition to topical/conceptual knowledge.

Final Thoughts

In my experience, most folks can wrap their heads around the idea of topical/conceptual knowledge as being a "thing." For the most part, folks are also relatively comfortable looking at topical/conceptual knowledge alignment. Perhaps you fit into this description. Where there rubber meets the road, however, is with cognitive complexity. So, that is where I shall end this blog, and it is where I will pick the next alignment foundation series blog. Until then, hit me up on Twitter, and happy aligning!


Gamoran, A., Porter, A. C., Smithson, J. L., & White, P. A. (1997). Upgrading high school mathematics instruction: Improving learning opportunities for low-achieving, low-income youth. Educational Evaluation and Policy Analysis, 19, 325-338.

Niebling, B.C., Roach, A.T., Rahn-Blakeslee, A. (2008). Best practices in curriculum, instruction, and enacted curriculum. In A. Thomas & J. Grimes (Eds.), Best practices in school psychology, 4(5), 1059-1072. Bethesda, MD: National Association of School Psychologists.

Porter, A C (2002) Measuring the content of instruction: Uses in research and practice Educational Researcher, 31, 3-14.

Webb, N.L. (1997). Criteria for alignment of expectations and assessments in mathematics and science education (Research Monograph No. 8). Madison, WI: National Institute for Science Education, University of Wisconsin-Madison.

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