Math and reading? Surely you jest!
Common Core Anchor Standards
(see chart below)
With the Common Core Standards, reading and writing stretches across the curriculum to all subject areas. One area that reading occurs naturally, but people may not realize it, is in math. March is Math Madness Month, so we are going to explore how reading and writing are integrated into the Math curriculum in the ELA Common Core Standards, and how the two sets of standards align with one another. The Common Core Math standards are pretty grade and topic specific, but the overarching themes among grade levels are called “Math Practice” standards. I won’t pretend to completely understand all of the other math standards, because I, in no way, fancy myself a math teacher, but I can see some pretty strong alignments between the MP standards and the ELA standards.
Apologies upfront for the visually unappealing post!
This is how I see the Math and ELA Standards aligning when it comes to word problems:
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
CCSS.ELA-Literacy.CCRA.R.1 Read closely to determine what the text says explicitly and to make logical inferences from it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.
CCSS.ELA-Literacy.CCRA.R.4 Interpret words and phrases as they are used in a text, including determining technical, connotative, and figurative meanings, and analyze how specific word choices shape meaning or tone.
CCSS.ELA-Literacy.CCRA.R.7 Integrate and evaluate content presented in diverse media and formats, including visually and quantitatively, as well as in words.
CCSS.ELA-Literacy.CCRA.R.10 Read and comprehend complex literary and informational texts independently and proficiently.
CCSS.ELA-Literacy.CCRA.W.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach.
While it is easy to make our own connections, it is clear that in order to comprehend any problem, be in ELA or Math, students must employ the same strategies: reading, comprehending, and making meaning of the words. I see the entire process of reading word problems to meet the ELA standard CCSS.ELA-Literacy.CCRA.R.10 Read and comprehend complex literary and informational texts independently and proficiently.
|CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.|
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
CCSS.ELA-Literacy.CCRA.L.3 Apply knowledge of language to understand how language functions in different contexts, to make effective choices for meaning or style, and to comprehend more fully when reading or listening.
As in ELA, much of Math involves understanding what is being asked in each question. What the question is asking relies heavily on connotation and word choice. Students must understand what they are being asked to do before even attempting to solve the problem. The words of math may differ from those of ELA, but domain specific words and content are important pieces of information.
CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
CCSS.ELA-Literacy.CCRA.W.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
CCSS.ELA-Literacy.CCRA.W.1 Write arguments to support claims in an analysis of substantive topics or texts using valid reasoning and relevant and sufficient evidence.
CCSS.ELA-Literacy.CCRA.W.2 Write informative/explanatory texts to examine and convey complex ideas and information clearly and accurately through the effective selection, organization, and analysis of content.
Being able to clearly explain how you solved the math problem is key in the new standards. Being able to explain your reasoning shows that you truly understand what was being asked of you. Students should be sure to explain differing solutions, and apply domain specific vocabulary.
CCSS.Math.Practice.MP5 Use appropriate tools strategically.
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
|CCSS.ELA-Literacy.CCRA.W.6 Use technology, including the Internet, to produce and publish writing and to interact and collaborate with others.|
Knowing when and how to use technology to solve a problem is key to both sets of standards, although not specifically stating, using the internet and appropriate tools to connect with other students and professionals to help collaboratively solve math problems is an amazing skills we need to teach our students.
CCSS.Math.Practice.MP6 Attend to precision.
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
CCSS.ELA-Literacy.CCRA.L.4 Determine or clarify the meaning of unknown and multiple-meaning words and phrases by using context clues, analyzing meaningful word parts, and consulting general and specialized reference materials, as appropriate.
CCSS.ELA-Literacy.CCRA.L.5 Demonstrate understanding of figurative language, word relationships, and nuances in word meanings.
CCSS.ELA-Literacy.CCRA.L.6 Acquire and use accurately a range of general academic and domain-specific words and phrases sufficient for reading, writing, speaking, and listening at the college and career readiness level; demonstrate independence in gathering vocabulary knowledge when encountering an unknown term important to comprehension or expression.
Some of these alignments apply specifically to word problems. Did you realize that by incorporating word problems into your curriculum, you are actually addressing 11 ELA Standards in addition to Math specific standards? I didn’t either, until I had to struggle with creating a post about math!
So, how can we put this new knowledge to work? The most obvious is to make sure you are incorporating word problems into your curriculum (something you surely already do). With all of the heat on Common Core recently, and the posts highlighting inappropriate math word problems (see Page 4, #15 or this Kindergarten Math Workbook as described by one parent, or this blog about the recent New York State Math Exams) how about by building our own Math Word problems? Better yet, have the students create their own! Shooloo is a pretty awesome tool that explains to students how to write word problems, and then lets them post their work, and practice with the work of others! How is that for authentic learning and collaboration?
To view the full set of math standards, please visit http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf