Building Them Up Through Literacy in Math

Math Literacy: An Integral Strand While Weaving the Basket of Learning

It wasn't so long ago that teachers were seen as the givers of knowledge who were meant to fill the empty vessel: the student. A great paradigm shift has taken place in education and the goal of the teacher is now known to be to build up the student with the many fabrics (i.e. facets) of learning in the model of weaving a basket. A facet of learning in the Math classroom that must not be overlooked in the regular incorporation of literacy in Math. You may ask yourself, "Did she mean to use the term 'numeracy' since she is referring to a Math classroom?" To that, my answer is an emphatic, "No!" Literacy in the Math classroom starts by making the concepts in Math accessible and meaningful to all of your students through the use of language, text, graphics and questions that put students in a position to ask meaningful questions and access information themselves. Chad Broome is an American middle school teacher who uses YouTube videocasts to showcase how Disciplinary Literacy in Mathematics can be used to encourage literacy in the Math classroom. Broome begins a new concept by showing the class a graphic or piece of text and then poses the questions, "What do you notice and what do you wonder?" By opening up the discussion in a conversational manner, students are encouraged to introduce their own thoughts and ideas based on their own observations and curiosities on the topic at hand. Through this approach Broome encourages neighbouring students to collaborate and identify trends and patterns in data presented and to formulate problem solving strategies based on their own reasoning and collaborative input from their peers. Broome encourages literacy in the classroom and uses it as a key strand in the fabric of higher order thinking that allows students to problem solve and ask important and meaningful questions of themselves and of each other. Students are able of asking and answering the 'big questions' if only we give them the opportunities and encouragement to do so!

Rhetorical or Meaningful; Are We Just Talking to be Heard?

We have all had that experience of knowing someone, whether it be in our personal or professional lives, who seems to talk and ask questions just to be heard. As educators, we should strive to make the direct questions we ask of our students effective and meaningful. There is great value in the use of open-ended questions where students are asked to dig deep and make their own connections to the topic at hand, however now I would like to consider strategies used to as effective and direct questions of your class. In their Literacy and Numeracy initiative, the Ontario Ministry of Education, published the Asking Effective Questions in Mathematics which can be accessed through the EduGAINS site.  A number of helpful guides to higher level question-asking for the Math classroom are featured and one example of such is pictured below:

Posing such questions allows for the students to make connections and allows them to make inferences and draw conclusions based on their observations and their reasoning skills. The use of prompts provides the opportunity for the teacher to give the student the floor to use their own voices to work out a problem verbally, justify and support their thought process, and essentially, to think out loud. If we want to welcome literacy into the Math classroom a great start would be to keep encouraging our students by leading them in a way that they become comfortable thinking out loud. 

Knowing Thy Impact

Knowing Thy Impact
John Hattie's work on Visible Learning is applied to Mathematics in his book titled Visible Learning For Mathematics: What Works Best to Optimize Student Learning.  In this book, the authors examine the plethora of "research-based" instructional practices in an effort to provide recommendations for best-fit teaching.  In a seminar in Toronto this summer, John Hattie recommended that educators resist getting seduced into a single form of instruction and opt for an understanding of the impact of various types of instruction to produce significant results and maximize student achievement.  He labelled it the Goldie Locks approach to instruction:"Not too hard and not too boring". This reminds me of Vygotsky's Zone of Proximal Development.  Matching instructional practices and strategies with the student's readiness to learn.  In sum, Hattie et al.'s framework asks the teacher to consider when particular teaching strategies are most beneficial, and where a student is in his or her understanding of a concept.

Making Algebraic Thinking Visible

Making Algebraic Thinking Visible

This clever problem would be an excellent way to lead student's into a dialogue about using different methods to solve a problem.  Further, it has an accessible entry where visually a student may be able to deduce the height of the table and it allows other student's to reason algebraically with multiple variables.  This could be used in an elementary class as an intro the algebraic inquiry, yet it could also be used as a "minds on" exploration in the senior grades before demonstrating how to solve equations with more than one variable.  Overall, it is a gripping challenge and would allow the students to engage in mathematical dialogic investigation.

Watch the video below by Presh Talwalker at Mind Your Decisions to see two methods to solve this problem.  It could also be solved using bar modelling from Singapore's Primary Mathematics program. 

Geometry Snacks

Geometry Snacks

I was intrigued by a geometry question I saw on  Twitter which credited authors, Ed Southwell and Vincent Pantaloni.  Geometry Snacks is a great mathematical puzzle book with many geometrical figures that will lead the student through several complex challenges.  The problems are fun, increase in complexity and allow students to see how many approaches one can use to solve a problem.  The first questions could be used to challenge elementary and middle school students, whereas the latter challenges involve the application of higher level mathematics and logic.  Once a student has solved the problem, the authors also provide further challenges. The rich geometric vocabulary makes this little pocket book, an excellent resource for teachers of Mathematics.


A Sample Question for Geometry Snacks as presented by blogger and author Presh Talwalker.

Sentences Stems

Sentence Stems - Helping Students to Participate in Academic Conversation

In our mathematics classrooms we want our students to have engaging conversations that encourage students to think critically about each other's ideas.  When students think critically they must challenge each other's responses and ask for clarification.  Being able to participate in scholarly conversation is a skill that needs to be taught; it's even more difficult for English Language Learners (ELLs) who are trying to learn the language and content at the same time.  This summer while taking my ELL Part 1 course I learned about the use of talk stems that provide students with sentence starters for initiating academic conversation.

A poster like this, hung on your classroom wall can be used as a form of reference for students when they are working in groups.  Making reference and modeling some of these sentence stems would be very beneficial in classroom discussion.

Poster taken from: https://mrlhuillier.wordpress.com/

Symbolab Friend of Foe?

Several of my students have been talking about the Symbolab website and Symbolab app for solving various math problems.  The site covers content in algebra, graphing functions, calculus, geometry, statistics, physics and chemistry.  Students can type in a problem or equation and pick from a list of solutions, complete with step by step instructions and explanations.  It is certainly a helpful tool when struggling to complete homework, but will students use it properly or simply right down solutions? After trying the Symbolab website for myself I have to say I'm impressed with some of its capabilities, however, I'm a little reluctant to recommend it to students because of the ads that keep popping up for dating sites.  Here is a screenshot of the solution provided to me when I typed  2x-y=8  and 3x+y=12 into the search bar. 

What do you think?