This is the fifth in a series of blog posts highlighting the digital literacies our students will need to succeed. The first four posts covered financial literacy, visual literacy, media literacy and historical literacy. This post will provide you with some ideas on how to infuse numeracy, one of the traditional literacies along with reading and writing, into the curriculum.
The thirteen literacies I feel need to be explored, practiced and mastered by students can be found in the graphic below.
Numeracy is the ability to reason and to apply simple numerical concepts. This includes, among other things, mastering of basic math, number sense, computation, measurement, and statistics. (In my grouping of literacies, I separate data literacy into its own category.)
The document entitle “Standards for Mathematical Practice” provide an extensive overview of the “varieties of expertise that mathematics educators at all levels should seek to develop in their students”. These standards “describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years”. It is about being able to take their mathematical skill set and use higher order thinking skills to evaluate, experiment, and reason. The Standards for Mathematical Process are:
- Make sense of problems and persevere in solving them: students analyze, conjecture, monitor and evaluate, transform, and conceptualize
- Reason abstractly and quantitatively: students decontextualize and contextualize as well as creating a representation of the problem
- Construct viable arguments and critique the reasoning of others: students can justify, reason inductively, and compare and defend
- Model with mathematics: students use their math skills to solve problems in everyday life
- Use appropriate tools strategically: students can pick the appropriate tool to help them
- Attend to precision: students label and present their mathematics in a way that make it understandable to others
- Look for and make use of structure: students can recognize mathematical patterns
- Look for and express regularity in repeated reasoning: students notice when calculations are repeated and use that information
In order to develop these levels of expertise in students, educators need to be able to connect the mathematical practices to the mathematical content in mathematics instructions. There are various ways to help this happen. There are the commercial textbooks and online products that can support student mathematical understanding. There are online mathematics informational sites to provide students with another “voice” to help them understand the basics a bit better and there are stand-alone software programs and apps to provide additional practice.
I am not a mathematics educator, so do not feel comfortable recommending software and apps to support mathematics instruction. I would not know if the app was reinforcing the skills in an appropriate way. However, I have created a PDF form entitled “Critical Evaluation of a Content-Based iPad/iPod App” (which could easily be used for Android apps, too). This form provides some guidance for teachers of any subject as they examine apps and tools to support instruction.
ONLINE MATHEMATICS INFORMATIONAL SITES
As with any online material, educators should preview the elements of the site to validate the information presented and methodologies being used.
- MathPortal is a site, created and written by a mathematician, which includes tutorials, formulas, sample assessments, and much more for upper middle school and high school students
- PBS LearningMedia includes material from PBS and also videos imported and streamed from Khan Academy. These videos can be searched by grade level and subject. No log-in is needed to view the videos and, since Khan Academy now requires a log-in, this site is an easy way for students of any age to access the Khan Academy videos without providing personal information.
- The National Council of Teachers of Mathematics provides support for teachers and vets online sites and lessons for use in the classroom. They also host the Illuminations site, one of the partner content collections that were a component of the now-closed Thinkfinity portal.
- It takes a while to comb through the plethora of links on Pinterest, but you can usually find a few gems!
TEXTBOOKS AND ONLINE PRODUCTS
Discovery Education has just released its Math Techbook. It is a great new addition to the Discovery Education and Discovery Streaming suite of tools and techbooks! This new digital textbook covers mathematics topics for grades 6-12. The secondary level includes Integrate Math I and II, Algebra I and II and Geometry. The Math Techbook uses an inquiry-based approach and real world problem solving to both engage students and have them understand the role mathematics plays in the “real world”.
There are interactive activities, videos, and embedded tools that are built-in to every unit of study. Students can have the text read aloud if necessary and create sticky notes to mark important points or to remember to ask a question. There are formative assessments that can help teachers easily differentiate math instruction for students and the Math Techbook works on computers and any mobile device.
The lessons and units are mapped to the Common Core State Standards, but will soon be available mapped to specific state standards for those not involved with the CCSS.
Some of the items that are accessible no matter where a student is in the Math Techbook are the interactive tools and the glossary.
I picked one sixth grade strand so you can get a feel for the components of each lesson and unit.
Do you have any great numeracy or mathematics resources you would like to share? Please feel free to comment and tell the rest of us about them! Thank you!