To have mathematical rigor, it is very important to provide a positive atmosphere where students are given ample time to collaborate, connect, learn standards at high levels and explain how they arrived at a particular answer. Gone are the days of teacher directed instruction with students remaining quiet in straight rows. Research has shown that instead, mathematics instruction is student-centered, collaborative and teacher facilitated.
"Confidence is Half the Battle"
How many people do you know that say they are not good at math? Take a minute to think why that would be. Many teachers give information to students and expect for them to think through problems exactly as they do without time for discussion with peers. This creates frustration and confusion for those who do not "get it" quite yet. There are other students who may seem to master a concept because they know how to follow directions and memorize the motions of the procedure, but when it comes to true comprehension, they are not able to meet the mark. One of the most important things that teachers can do is respect their student’s thoughts, ideas and individuality by making sure they know that everyone can do math and there are multiple ways of going about finding solutions. Confidence is half the battle.
Wait!
Wait time is one of the most important strategies that teachers should intentionally and consistently use to build confidence for students. It may actually feel uncomfortable to the teacher, as well as the student at first. However, the uneasiness will become second nature. This will gently force students to participate and have a voice. It may seem like an eternity, but teachers should give at least three seconds for the students to hear the question, process the answer and formulate a response. If the teacher does not call on a particular student, the one who answers the question is most likely just a faster processor. He may or may not understand the material more than his peer. Answered correctly or not, it is important for all students to feel comfortable and respected while participating. Many of the other students are still processing, so the teacher should provide several seconds after the first response before validating, asking for more, or moving onto the next question. If they do this, it may even provide students with opportunity to piggyback on other student’s responses and add important, well-mannered, rich discussion.
Take a minute to view this YouTube video on wait time and wait time extended. Can you tell the difference? How can this strategy help students think critically?
Learner-Centered Environment
Collaboration is another strategy for providing assurance. For instance, if a teacher poses a question to the class, the students can talk within their group about the solution prior to being called on in front of the entire class. It offers a learner-centered environment with a built in safety net for shy or unsure students, allows them to share ideas and see how others think through mathematical situations, and encourages meaningful math talk. If a teacher is allowing for collaboration, all students are participating and learning at higher levels.
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| Mrs Gore's 5th Grade Classroom |
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Connections to vocabulary, past experiences and other disciplines is another important strategy for teaching mathematics. Students need to be provided with key vocabulary at the beginning, middle and end of the lessons so that it is infused in their mind. Teachers may use other words to connect, but it is very important to consistently use actual math vocabulary words, so as to familiarize students and prevent misconceptions. There should always be "math talk" in a math classroom. A few good vocabulary strategies are word walls, graphic organizers, songs and Frayer models. The best way for students to remember vocabulary is to make it fun.
Be Very Familiar With Your Curriculum!
Learning standards at high levels is critical. Teachers must be very familiar with their curriculum and teach it in multiple ways at higher levels so that students understand all concepts forwards and backwards. Many teachers stop using best practices and begin a teacher-centered model when they reach a more difficult concept. This most often happens because fear of giving up control to messy and free-ranging strategies and activities when there is little time to get through the material. A common, but critical mistake is to revert to the direct teach, drill and kill model. In order for students to truly learn to a deep conceptual level, teachers must first peak the curiosity of students, then provide them with various thinking strategies. These may include, connections to prior knowledge, multiple representations, risky situations, open-ended questions, spiraled content, collaboration, linking concrete to abstract, differentiation, scaffolding and a building understanding all the way up to the higher levels of Bloom’s Taxonomy. Mathematical content should then be spiraled back into the instruction at least three times during the year.
There should always be a connection via another discipline, such as literature, built into a mathematics classroom which provides a way for students to organize their thoughts and justify their answers. An example that teachers may use is to provide a reading for students and have them work through a real-world problem. They should work collaboratively to solve the problem, which would have multiple solutions or ways to solve. Students should brainstorm together, journal, etc. to find a common path to solve the problem. They may even act it out in order to solve the problem or create their own.
Rigor in Education:
Higher-Level Thinking, Safe Environment, Engaging, Consistency, Risk, Thought Provoking, Real-Life Problems
The road to rigor includes quality instruction with a deep level of learning, with students asking and answering higher level questions in a safe environment. Permitting slight discomfort provides ownership. Utilizing manipulatives creates a bridge to a deep level of interest and comprehension. Misconceptions are prevented by consistently connecting vocabulary in creative ways. Risk delivers confidence over time, because people learn from mistakes. All of this causes students to “think” critically about mathematical concepts, enjoy the process and become life-long learners, who can strategically apply their learning into their everyday lives.
