Creating Authentic Mathematics Learning Contexts
What is the purpose for creating Authentic Mathematics Learning Contexts?
The purpose of creating authentic mathematics learning contexts when teaching mathematics concepts/skills/strategies is to explicitly connect the target math concept/skill/strategy to a relevant and meaningful context, therefore promoting a deeper level of understanding for students.
What does it mean to create Authentic Mathematics Contexts?
Creating authentic contexts within which to teach targeted mathematics concepts/skills/strategies requires teachers to think of ways the mathematics concept/skill/strategy occurs in naturally occurring contexts that hold meaning for the students they teach. When doing this, it is helpful to consider your students' age-related interests, cultural/community interests, and common experiences your students share. Using the Mathematics Student Interest Matrix & Mathematics Class Interest Matrix described below can be of great assistance in matching meaningful contexts for your students with the particular mathematics concepts/skills/strategies you typically teach. Examples of authentic contexts include naturally occurring contexts in the school environment (e.g., lunch counts - counting, addition, subtraction, graphing); activities that students typically engage in that they find interesting (e.g., shopping at the mall for music CDs - comparing geometric shapes: round CDs, square CD containers, etc; greater than/less than - number of "Hip Hop" CDs compared to number of country CDs; family or cultural oriented activities (e.g., family dinner - multiplication/division situation using combinations of dinner utensils - 3 eating utensils for 4 family members each equals 12 eating utensils total).
Creating authentic mathematics contexts can be a wonderful way to make mathematics meaningful to all students, however, for students with special needs the authentic context must be explicitly connected to the target mathematics concept/skill/strategy. This is important because students may focus on the context without connecting the context to the learning objective. Learning characteristics such as attention problems, cognitive processing deficits, passive learning and metacognitive deficits predispose students to "miss" the connection between the context/activity and the mathematics concept/skill/strategy they are supposed to learn. To ensure students make this connection, teachers must explicitly model the concept/skill/strategy within the authentic context and clearly demonstrate how the concept/skill/strategy relates or is applied. See the Teacher Tool, Explicitly Model Mathematics Concepts/Skills and Problem Solving Strategies" for ideas on how to do this.
Using Technology to Create Authentic Contexts: Incorporating technology such as videotape and teaching simple video editing to students provides another tool for developing authentic contexts for learning mathematics concepts/skills. For example, students could be provided a whole number operation to illustrate using video (e.g. 5 x 4 = 20). Then, in small groups or individually, students would develop a "movie script/scene" they could videotape that would illustrate the operation, in this case the multiplication process. After shooting the video and then editing it, students could present it to the class and describe how the video illustrates the particular mathematics concept/skill they were assigned.
To find out about additional ideas for integrating technology in ways that provide students authentic learning contexts, visit the Internet resources listed below:
Florida Center For Instructional Technology, "No Strings Attached!"
Visit No Strings Attached! for wireless laptop lesson plans and student activities that seamlessly integrate wireless technology. Also find practical classroom management and tech tips to facilitate the wireless classroom and teacher and students reflections on the impact of wireless technology in the classroom.
Apple Education Site
View online resources for improvement in education. See how digital media and a web-based student information system can help improve learning.
What are some important considerations when creating Authentic Mathematics Contexts?
- Use contexts that are meaningful for the students you are teaching (age, interests, experiences). Contexts may be school related, family related, or community related.
- Use the Mathematics Student Interest Matrix and Mathematics Class Interest Matrix to assist you in developing authentic contexts that are appropriate for your students and that match the particular mathematics concepts/skills/strategies you teach (see description below).
- Explicitly model the target mathematics concept/skill/strategy within the authentic context.
- Clearly demonstrate the relevance of target mathematics concept/skill/strategy to the authentic context.
- Provide students with the opportunity to practice the target mathematics concept/skill/strategy within authentic contexts after appropriate teacher modeling. Monitor student as they practice, provide them specific corrective feedback, remodel as needed, and provide positive reinforcement for accuracy and for effort!
How do I implement Creating Authentic Mathematics Contexts?
- Teacher chooses appropriate context within which to teach target math concept/skill.
- Teacher activates student prior knowledge of authentic context, identifies the math concept/skill students will learn, and explicitly relates the target math concept/skill to the meaningful context.
- Teacher explicitly models math concept/skill within authentic context.
- Teacher involves students by prompting student thinking about how the math concept/skill is relevant to the authentic context.
- Teacher checks for student understanding.
- Students receive opportunities to apply math concept or perform math skill within authentic context. Teacher monitors, provides specific corrective feedback, remodels math concept/skill as needed, and provides positive reinforcement.
- Teacher provides review and closure, explicitly re-stating how the target math skill relates to the authentic context and remodeling the skill.
- Students receive multiple opportunities to apply math concept or practice math skill after initial instructional activity.
How does Creating Authentic Mathematics Contexts help students who have learning problems?
- Creating Authentic Mathematics Contexts facilitates student conceptual understanding by explicitly connecting math concepts/skills/strategies to meaningful experiences, thereby facilitating the likelihood that students will both remember what they have learned and be able to extend their understanding throughout the concrete-to-representational-to-abstract sequence of mathematical understanding.
- Explicit instruction/modeling provides necessary cueing to prevent students from missing important conceptual features/problem-solving steps/elements due to attention problems, memory problems, etc.
- Authentic contexts can motivate students by creating for them relevance and novelty.
The Mathematics Student Interest Matrix and The Mathematics Class Interest Matrix
Description. The Mathematics Student Interest Matrix provides you an informal process for finding out what kinds of activities, topics, etc. are of interest to your students and/or that represent meaningful experiences in their lives. The matrix can be completed by simply asking your students to individually share their interests, family activities, hobbies, etc. using the Mathematics Student Interest Matrix. Students can either complete it by writing or drawing or they can dictate their ideas to a peer (if a student has sensory-motor or written expression difficulties). Students can also complete the Mathematics Student Interest Matrix in small groups while playing a board game where students move by responding to questions about their interests, family activities, hobbies, etc. and having a group recorder write down the responses. Once students have completed the Student Interest Matrix, the teacher can review it and complete The Mathematics Class Interest Matrix. When completing this, the teacher can then determine the mathematics concepts they teach that can be related to the various interests of the students in their class. This matrix can then be used for planning purposes when creating authentic mathematics contexts for teaching particular mathematics concepts/skills/strategies. Examples of both matrices are illustrated below.
What are additional resources I can use to help me implement Creating Authentic Mathematics Contexts?
MathVIDS is an interactive CD-ROM/website for teachers who are teaching math to students who are having difficulty learning mathematics. The development of MathVIDS was sponsored through funding by the Virginia Department of Education.