Building Schema
Chapter 3 "Build Schema"
In Chapter 3 of Rigor by Design, Not Chance, author Karin Hess expresses the importance of schema being intentionally addressed in lessons due to being an essential component in "dramatically expanding a learners knowledge base" (Hess, 2023, p. 104). Hess quotes Barbara Oakley, Beth Rogowsky, and Terrance Sejnowski's description of "Schemas" as a "quintessential form of prior knowledge …. Schemas shape our thoughts about what we are learning … and allow new learning to be more easily placed in with other, previously learned material" (2023, p. 103-104).
Schema plays a crucial role in our expansion of knowledge as new information overloads our working memory when our brain lacks prior knowledge, subsequently lending to information that "often doesn't stick" (Hess, 2023, p. 105). Hess explains a teacher's role in guiding the building of schema as considering unifying concepts and essential skills, how these pieces relate to the overall genre, what prior knowledge exists, if any, and the potential of misconceptions (2023, p. 106). Schema is most commonly built through the following mental models: structural which refers to the organization of knowledge, and procedural which refers to the steps necessary when completing a process.
Following the reading, I chose to look further into Schema Built Instruction in the elementary setting. I chose this topic due to its relevancy to my primary education degree. Within my search, I found the article The Effects of Simplified Schema-based
Instruction on Elementary Students’
Mathematical Word Problem Solving
Performance by Houbin Fang, Sherry Herron, Qi Zhou, Taralynn Hartsell, and Richard Mohn featured in Education for All: Journal of Mathematics Education. In addition to its relevance to my degree, it highly relates to my current classroom placement which is a math room composed of third grade students testing into the low end of mathematic ability.
The Effects of Simplified Schema-based Instruction on Elementary Students’ Mathematical Word Problem Solving Performance features the study of Simplified Schema Based Instruction (SSBI), a modified Schema Based Instruction, with general education second grade students when solving one-step addition and subtraction word problems. The modification of Schema Based Instruction into SSBI was done in an effort to tailor the strategy into one more developmentally appropriate for the younger learners. The strategy behind SSBI was to teach the learners to solve word problems by recognizing the underlying structure of the problem which "is very important to problem 'comprehension and representation'" (Fang et al., 2015, p.38). Word problems were targeted within the study as "according to National Assessment of Educational Progress (NAEP), word problems have become a very difficult area for students across ability and all age levels" despite researcher's efforts in developing "effective word problem solving instruction" (Fang et al., 2015, p. 38). "In addition, the investigators also intended to discover if participants could maintain SSBI strategy after the intervention terminated" (Fang et al, 2015. p. 41). During intervention, the learners were taught to solve the word problems using four steps- Step 1: read the word problem out loud while identifying the larger number, smaller number, unknown number, and label of interest, then rephrase the problem in your own words, Step 2: fill in the given diagram with the larger and smaller numbers followed by the label, Step 3: decipher the operation choice using the instructions "if the total or the sum of two numbers is unknown, addition is the choice of operation; however, if the total is known and the problem is to find one of the smaller numbers; or if the difference between two numbers is asked for, subtraction is required to solve the problem" (Fang et al., 2015, p. 43), and Step 4: solve the equation and check the answer. The learners were taught using one worksheet containing five word problems per session, then required to solve the same five problems independently. The figure below shows participants' performance in all phases. "Participants' performance in word problem solving immediately increased during the intervention. Researchers also found that participants remained SSBI skills at a high level during maintenance phases (92% on average). Therefore, SSBI cannot only help students with their word problem solving, but also can be mastered by students" (Fang et al., 2015, p. 49).
The Effects of Simplified Schema-based Instruction on Elementary Students’ Mathematical Word Problem Solving Performance features the study of Simplified Schema Based Instruction (SSBI), a modified Schema Based Instruction, with general education second grade students when solving one-step addition and subtraction word problems. The modification of Schema Based Instruction into SSBI was done in an effort to tailor the strategy into one more developmentally appropriate for the younger learners. The strategy behind SSBI was to teach the learners to solve word problems by recognizing the underlying structure of the problem which "is very important to problem 'comprehension and representation'" (Fang et al., 2015, p.38). Word problems were targeted within the study as "according to National Assessment of Educational Progress (NAEP), word problems have become a very difficult area for students across ability and all age levels" despite researcher's efforts in developing "effective word problem solving instruction" (Fang et al., 2015, p. 38). "In addition, the investigators also intended to discover if participants could maintain SSBI strategy after the intervention terminated" (Fang et al, 2015. p. 41). During intervention, the learners were taught to solve the word problems using four steps- Step 1: read the word problem out loud while identifying the larger number, smaller number, unknown number, and label of interest, then rephrase the problem in your own words, Step 2: fill in the given diagram with the larger and smaller numbers followed by the label, Step 3: decipher the operation choice using the instructions "if the total or the sum of two numbers is unknown, addition is the choice of operation; however, if the total is known and the problem is to find one of the smaller numbers; or if the difference between two numbers is asked for, subtraction is required to solve the problem" (Fang et al., 2015, p. 43), and Step 4: solve the equation and check the answer. The learners were taught using one worksheet containing five word problems per session, then required to solve the same five problems independently. The figure below shows participants' performance in all phases. "Participants' performance in word problem solving immediately increased during the intervention. Researchers also found that participants remained SSBI skills at a high level during maintenance phases (92% on average). Therefore, SSBI cannot only help students with their word problem solving, but also can be mastered by students" (Fang et al., 2015, p. 49).
This study is a wonderful example of intentionally incorporating schema into lessons, as mentioned by Hess in Chapter Three of Rigor by Design, Not Chance. This study also verifies the importance of schema as reiterated by Hess throughout the chapter. In this example, schema created a deeper understanding, represented by the successful completion of word problems, which ultimately led to a skill that stuck. The steps utilized in the study, as mentioned above, also closely mimick Hess' procedural schema for word problems on page 111. Here, she mentions to solve word problems using schema through the following procedure: "read the problem for key words or phrases", "determine what's being asked and identify the operation needed" (she also mentions the use of possible visuals or tools that may help in this step which in the study was the given diagram), "list related math terms or symbols and any operations or concepts that will help solve the problem", "perform the operation, check my calculations, and show my work", and "explain in two or three sentences".
Overall, The Effects of Simplified Schema-based Instruction on Elementary Students’ Mathematical Word Problem Solving Performance support Hess' statements in Chapter 3 of Rigor by Design, Not Chance "Building schemas is really important" and "Schemas become frameworks for learning new content and dramatically expanding a learner's knowledge base" (Hess, 2023, p.104). In addition, the study is a reminder of the importance of intentional rigor in a classroom, in this instance accomplished using schema.
Fang, H., Herron, S., Zhou, Q., Hartsell, T., & Mohn, R. (2025). The Effects of Simplified Schema-based Instruction on Elementary Students’ Mathematical Word Problem Solving Performance. Journal of Mathematics Education, 8(1), 37–55. https://doi.org/Education for All
Hess, K. (2023b). Chapter 3: Build Schemas. In Rigor by Design, Not Chance: Deeper Thinking Through Actionable Instruction and Assessment (pp. 104–134). essay, ascd.
I agree that this article has direct connections to Hess' arugment, and it also shows that "teaching the test" is often mischaracterized and is simply helping students build procedural schema for learning tasks.
ReplyDeleteI found this study's findings very interesting. When students have a systematic way of solving problems, it makes it much easier for them and can provide a life-long framework of problem-solving in certain contexts. This was an excellent blog post!
ReplyDeleteI really enjoyed reading your blog post this week. I think the data you incorporated from the articles was interesting to see. Being a math teacher it has been prevalent that the more relatable I can make a lesson the better it goes. I've been trying to connect my lessons to the real world more and more by having students look at baking with scale factors and proportions as well as building and structures. We also used legos to work on proportions as well all these things the students really enjoyed. Today my students had a formative assessment on these skills and the scored fairly high so I'm excited to see how the lesson work long term and how well this knowledge sticks to their long term memory.
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