5 Types of Knowledge Used to Construct Meaning in Math


We see it in media everywhere: American students are not able to compete with students from other countries, especially in the areas of math and science. People are becoming increasingly concerned that students do not have the skills they need in order to be successful in a global economy. Whether you agree with these statements or not, one thing is certain: teachers carry an immense responsibility to give our children a solid foundation so they can become productive members of society.




In Building Mathematical Comprehension (2011), Laney Sammons helps teachers learn to apply common strategies for reading instruction towards math instruction.  She explains that while skillful readers actively construct meaning using what they know about content of a text and its context, mathematical comprehension is twice as challenging. Not only do students need to be able to understand the concepts, but they also need to be able to read and comprehend the text itself. I love this approach because students can take what they have learned about reading strategies and apply it to other subjects!

There are 5 types of knowledge students draw upon to construct mathematical meaning: content knowledge, structural knowledge, pragmatic knowledge, situational context knowledge, and (what I am calling) intrinsic knowledge. I will share about each type of knowledge below, how we can apply it to math instruction, and some practical classroom activities that you can implement during math! 



CONTENT KNOWLEDGE:


We Know: When readers are more familiar with the content, it is much easier for them to construct meaning. This prior knowledge provides a foundation for understanding and building new knowledge.

Math Application: Students need a foundation of prior knowledge to build upon in order to make connections and construct meaning. Any time we can focus on what students already know about the content, we give them valuable opportunities to build upon that knowledge and make lasting connections. 

Related Math Activities to Build Content Knowledge: Schema Maps, Inference Maps, Text Walks





STRUCTURAL KNOWLEDGE:

We Know: Skilled readers use knowledge of text structures to build meaning. For example, when reading a narrative text, a skilled reader knows to look for important details about the characters, setting, and plot development. When reading an informational text, skilled readers know to pay attention to how the information is organized, whether it's organized chronologically, most important to least important, or by topic. 

Math Application: Students need to understand how word problems are structured. I love the idea of treating word problems like a unique genre of text!  In most cases, word problems begin with introductory information to provide context which may or may not be important to solving the problem. This is followed by factual details that are important for solving the problem. The main idea (or what they need to determine) often comes at the end of the problem. Knowing this structure can really help kids begin to problem-solve more effectively. In addition to understanding how word problems are structured, the students also need to understand how mathematical concepts are structured. 

Related Math Activities to Build Structural Knowledge: Explicit instruction about the text structures of word problems with repeated practice applying that structure 



PRAGMATIC KNOWLEDGE:

We Know: Skilled readers also use their life experiences to construct meaning of the text. Students with different life experiences may interpret the same text with different meanings based on their unique life experiences. 

Math Application: Students come to our classroom with problem-solving strategies based on their own life experiences. We should respect their different attempts to problem-solve because it will increase their confidence and willingness to take risks. 

Related Math Activities to Build Pragmatic Knowledge: Think/Pair/Share and Class Discussions to give students opportunities to explain their problem-solving process to one another



SITUATIONAL KNOWLEDGE:

We Know: Skilled readers know that situational context will change the way they read a text. For example, reading a poem for enjoyment will result in a different approach than reading a poem to analyze its meaning. Skimming a non-fiction text to find a few important details will result in a different approach than reading a non-fiction text to analyze if the author's point of view supports their own point of view. 

Math Application: Students need to become aware that situations also provide context when solving a math problem. When the directions ask students to estimate sums and differences, their approach to solving the problems should be different than when the directions as to solve for sums and differences. The directions are a great place for students to look for situational context, but so often they are overlooked! 

Related Math Activities to Build Situational Knowledge: Set the purpose for problem-solving, Draw attention to the directions to provide situational context (ex: estimating versus solving)



INTRINSIC KNOWLEDGE:

We Know: When students feel confident about how to do something, their interest and motivation begins to climb. As interest and motivation climbs, they want to practice more, which in turn, better develops their skills. Skilled readers often have a positive attitude towards reading and believe that reading is valuable. The believe they are capable of reading and understanding. They realize that understanding the text results from putting forth effort and persevering through challenges, not just because they were born a good reader. 

Math Application: Students' perception about math is so important! Do they see themselves as capable mathematicians and doers of math? This is so key. "When students believe their efforts determine their achievement rather than just their innate ability, they are more persistent in their mathematics learning and, thus, are more successful" (Sammons, 2011, p 26). We must help our students develop a positive mindset towards problem-solving. We must help them see that math makes sense and is valuable. We must help them begin to see themselves as capable mathematicians and doers of math. 

Related Math Activities to Build Intrinsic Knowledge: "I am a Mathematician" Self-Portrait or Poem (including qualities that demonstrate they are mathematicians), Attitudes/Beliefs Inventory Survey



I am so excited to dive deeper into this content and share ideas about how to improve our math instruction. I will be sharing posts in the future that go more in-depth with specific reading strategies that can be applied to math instruction and what that practically looks like in the classroom. I sincerely hope you find this series to be helpful to you for increasing your skills as a math teacher. I know this book has already taught me so much!

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