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Understanding Standards: Content, Cluster, Domain, Process and Practice

Let’s think about language. If someone, for instance, were to memorize the entire Spanish dictionary, could they claim to speak Spanish? Clearly not. It takes more than just knowing words and their meanings; we also need a structure that gives them meaning—a grammar, an orthography, and even a body of literature that helps us truly appreciate the language.

In this metaphor, the words in the dictionary represent mathematical contents. They are essential, and we should strive to create activities or learning situations that cover the curriculum’s knowledge. However, that alone is insufficient. The content – whether calculating a remainder, finding the area of a polygon, analyzing the probability of an event, or exploring the derivative of a function – comes to life when combined with these processes. As the Principles and Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM, 2000) describe:

The Content Standards—Number and Operations, Algebra, Geometry, Measurement, and Data Analysis and Probability—explicitly describe the content that students should learn. The Process Standards—Problem Solving, Reasoning and Proof, Communication, Connections, and Representation—highlight ways of acquiring and using content knowledge. (p. 29)

Moreover, these standards were deepened through some practice standards by the Common Core (CCSS, 2010), once the US adopted such framework in the official state curriculums, ten years later.

In any case, as we delve deeper into curricular documents, we encounter more specific terms that are essential to understanding the framework of math education. The challenge is that these terms are intertwined, their definitions can be nuanced, and their application can change over time. Nevertheless, if you are familiar with these terms, you can jump to the next section!

To help us navigate this intricate sea, let’s map out these terms in comparative tables, with some examples from K-5 and definitions.

Let’s start from the beginning: contents are those concepts that our students must know and eventually master.

 

Definitions contents

 

These terms are key to read standard identifiers in official documents. They are always as follows: Grade number, Domain initials, Cluster

letter, Performance Expectations number (and letter, if needed).

For example:

4.NF.B.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

4 → Grade: 4th
NF → Domain: Number and Operations – Fractions
B → Cluster: B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers
→ Performance expectation: 3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

To recognize the domain initials, it is key to keep in mind the different domains we have. As we will see in a minute, the first major change in the NJSLS (New Jersey Student Learning Standards) for 2023 is reshaping a bit the following list. Colors help to understand links between both lists.

 

Domains

 

Once we know how to read this kind of identifiers, it’s time to look beyond content. What’s the difference between ‘process’ and ‘practice’? We could say that process standards from NCTM (2000) evolved into practice standards as they became part of the Common Core. In essence, they refer to the same ideas, as we can see below.

 

Process

In Conclusion

Navigating the terrain of educational standards might initially seem like an overwhelming task. Much like mastering a new language, it requires an understanding of vocabulary, grammar, and structure. Yet, as we unpack the meaning of these terms – content, cluster, domain, process, and practice – and start to see how they interact and build upon each other, we begin to appreciate the richness and depth of mathematical education.

These standards do not exist in isolation. Just as words in a dictionary become more than their individual meanings when woven into sentences and stories, these standards come to life when applied to practical, real-world contexts that deepen students’ understanding and appreciation of mathematics.

In any case, it is important to remember that these guidelines are not meant to stifle creativity or individual teaching styles. Instead, they should be viewed as a tool – a roadmap that guides us towards the shared goal of equipping our students with the mathematical knowledge and skills they will need to navigate an increasingly complex world.

  • Albert Vilalta

    Trained Engineer and a vocational Mathematics Professor. Currently he is a professor in the Education department of the Universidad Autónoma de Barcelona and is finishing a doctorate in Mathematics Education. He combines his university roles with teacher trainings and, above all, his investigation, communication and conceptualization responsibilities in the education department of Innovamat.

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