The Common Core State Standards for Mathematics (CCSSM) include two sets of standards that were designed to be taught and applied in an integrated way – the Standards for Mathematical Content and the Standards for Mathematical Practice. The Standards for Mathematical Content are grade-specific standards that describe math content students should master at each grade level. The Standards for Mathematical Practice are eight processes or practices that mathematically proficient students use regularly. These eight practices are not content-specific. They focus on how students go about doing math and should be integrated in all math content at all grade levels. As teachers and students engage with the Standards for Mathematical Content, they should be employing the Standards for Mathematical Practice to do so.
The Standards for Mathematical Practice provide a springboard for students, teacher teams, and schools to develop a common language around working with mathematics. In the past, teachers within and across grade levels or departments may or may not have developed common ways of talking about and doing math. These eight practices offer guidance as teams of teachers share teaching practices and resources for teaching the CCSSM. As students apply the practices to their work with mathematics from year to year, they will gain a more coherent and connected learning experience.
Using Student Blogs to Develop Proficiency
There are numerous technological applications available that can support teachers and students as they think about, talk about, and do mathematics using the eight practices which are described below. They include tools such as virtual manipulatives, presentation software, and collaborative tools like wikis and blogs. In this article, I make a case for student blogs as a tool that can support and extend students’ mathematics proficiency through the Standards for Mathematical Practice. Teachers who use math journals can easily convert that process to a digital one through blogging. Blogging is a versatile process that can be implemented in one grade level or math course or across grade levels as students progress through more difficult math content from year to year. Additionally, blogging can be a private or public process. Teachers and students can determine which posts to use for private blogging and which to share with others. In either case, the teacher can monitor students’ application of these mathematical processes and provide ongoing feedback on not only the product of students’ work with mathematics but also on students’ thinking about mathematics. The act of blogging allows for:
- students to make their thinking visible
- students and teachers to give one another feedback
- students and teachers to keep a record of student progress with mathematics
What follows is a definition of the eight Standards for Mathematical Practice and a description of how blogging can enhance and strengthen students’ use of these practices:
Teachers who use math journals can easily convert that process to a digital one through blogging. Tweet
1. Make sense of problems and persevere in solving them
Students who make sense of problems and persevere in solving them can analyze problems, design and implement solutions for addressing them, and monitor their own progress toward a solution. Perseverance in problem solving involves the ability to adjust strategies and tools as needed. The act of blogging can be a process through which this problem solving and perseverance comes to life. Rather than thinking of blogging as the product of mathematical thinking, a blog post can be the avenue for the thinking to occur. Students who are verbal processors will benefit from the opportunity to flesh out their thoughts in print. In addition, blogging may make it easier for a student to identify misconceptions or errors in his/her thinking and revise the approach to a given problem.
2. Reason abstractly and quantitatively
This practice involves two processes – contextualizing and decontextualizing. Contextualizing is the act of applying context to a given problem, while decontextualizing is the process of removing a problem from context in order to manipulative the variables involved. A blog post could be constructed in which students design and describe a meaningful context for a given problem that is presented without context. Students can also be encouraged to include media to further elaborate on their self-generated context. Conversely, a context-based problem can be decontextualized as students blog about the process of identifying and manipulating important variables to arrive at a solution to the problem.
3. Construct viable arguments and critique the reasoning of others.
As students design processes and select tools and strategies for solving problems, this practice requires them to justify their thinking and evaluate their classmates’ thinking. In order to apply this practice, students will need to have access to classmates’ blogs. A classroom that is aligned with the expectations of the CCSSM will encourage divergent thinking and problem solving. Students should be encouraged to construct processes that work for them while being held accountable for justifying their work with mathematics. A blog post can be written as a justification of a student’s approach to a particular problem and should include multiple types of support for the student’s argument (i.e. written, visual, graphic, and algebraic expressions). Students can critique the soundness of their classmates’ arguments through blog comments, and students can be given the opportunity to revise their work based on the feedback of others.
4. Model with mathematics.
Through modeling with mathematics, students learn to apply math concepts and skills to authentic, real world examples. Students can create concrete, pictorial, verbal, or expressive models in addition to designing scenarios that apply meaningful contexts to problems. Blogs are versatile in that students can upload a variety of types of digital media as models (i.e. photographs, drawings, algebraic expressions, videos). Concrete models, such as those involving manipulatives or real life objects, can be photographed or recorded through video and uploaded to students’ blogs as well. Students can be encouraged to comment on their peers’ blogs and provide a different model or representation of the same concept or skill. Through this process, students can learn to think about and represent mathematical concepts in diverse ways.
5. Use appropriate tools strategically.
Before students can select appropriate tools for working with mathematical concepts and procedures, they first must be familiar with a variety of tools and their purposes. After frequent modeling of a variety of tools available to mathematicians, students will develop the ability to strategically select tools to serve specific purposes. A blog can be the avenue through which students justify the tool that was selected for a specific problem or situation. Additionally, students can blog written, visual, or graphic instructions for using specific tools for specific types of math problems. Comments can be used to question and critique a student’s tool selection or recommend a different tool for the same purpose.
6. Attend to precision.
Precise thinking and expression is key to mathematicians, and should be an expectation in math classrooms. This includes the use of correct terminology and appropriate units of measurement as well as the ability to clearly articulate mathematical processes. Precision could easily be incorporated into a feedback system and grading rubric for students’ math blogs. As students and teachers comment on one another’s blogs, feedback can be provided regarding the precision of the blog post. Commenters can ask for clarification regarding units of measurement, processes involved, or tools used in the problem solving process. When students are aware that accurate communication is an expectation and that classmates or teachers may question their thinking and explanation, they may tend to write more clearly in their initial posts.
7. Look for and make use of structure.
By encountering and persevering through numerous mathematical problems over time, students will begin to recognize structure and patterns among certain types of problems. This ability to identify structure within and across problems and use that structure to assist in the problem solving process can be developed through blogging. A blog provides an ongoing record of students’ thinking and work with mathematics. Students can quickly and easily review previous blog postings, searching for patterns among specific problem types, concepts, or scenarios. Most blog sites offer a search feature that would allow students to quickly locate terms, concepts, tools, or strategies from past blog postings. The purpose of identifying structures and patterns within and across problems is to assist students with solving new problems that make fit those patterns or trends.
8. Look for and express regularity in repeated reasoning.
Using regularity in repeated reasoning involves examining the reasonableness of results and making generalizations from processes used to solve problems. As students approach a solution to a given problem, they should continuously evaluate the reasonableness of their own thinking and adjust their processes if needed. As students make their thinking visible through blogging, they may be able to more easily reflect on the accuracy of their thinking and recognize when adjustments need to be made. Peer feedback through blogging can also facilitate this reflective process. Blogging can also assist in making generalizations regarding the tools and processes used across a variety of types of problems.
Putting it into Practice
Let me close by addressing a few things you may be wondering.
What if my students don’t have regular access to technology?
If your students don’t have daily access to technology for blogging, use a math journal or notebook for daily work with the Standards for Mathematical Practice. When you do have access, students can select entries from their math journals to add to their blogs. That time can also be spent commenting on classmates’ blog posts.
What are some good sites for student blogging?
Kidblog.org is a free, safe blogging site for schools. Teachers control and monitor student blogs. All student blogs are private by default, but teachers can choose to make certain posts public or share them with parents. Edublogs.org is a secure blogging site that provides different levels of paid accounts depending on the number of teachers using the subscription. A teacher with a Pro account can maintain an unlimited number of student blogs.
How should students structure their blogs?
The structure of each student’s math blog will vary according to grade level, teacher expectations, and student preference. All posts will be dated, which adds a chronological organization to each blog. In addition, students can tag blog posts with keywords, making it easier to organize and locate previous posts. Teachers may set specific expectations for post structure in terms of length, incorporation of digital media, etc.
Image courtesy of Flickr, Peter Rosbjerg