Student Choice
"Give the pupils something to do, not something to learn; and the doing is of such a nature as to demand thinking; learning naturally results."
--John Dewey
- Redistribution of Power: The teacher acts as a facilitator who shares the power with the students by including them in decisions as to how their learning environment/classroom structure should be set up and by providing them with the tools they need to succeed. The teacher must set adequate parameters that provide a cooperative learning environment but also include students on every facet of the course. Instead of focusing on grades and tests, the facilitator must help the learners learn to reason, communicate, and develop social and personal responsibility, self-awareness and a capacity for leadership. With shared power, the teacher and learners must be highly reflective, constantly questioning and assessing how to improve the teaching and learning. This design allows for more productivity. Since the learners have control over their own destiny and are responsible for the outcome, they are more likely to work harder.
- Students are Responsible for Their Own Education: Students must be given a choice in their learning experiences and learning environment. If they help choose their curriculum and decide on the rules in the classroom, they will achieve ownership of their learning, have pride in their participation, obtain self confidence, and exhibit higher levels of cognition and metacognition. By having the learners keep track of their own progress and growth, they fully aware of their learning outcome, which is empowering. They can take charge if their destiny by assessing their current understanding, creating a plan to move forward, and putting the plan into action. This design allows for higher levels of achievement and gives the learners authority, power, belonging, and love, and allows them to realize their intellectual potential.
- Belonging: By providing learners with choice a safe learning space is created-- they design it, they decorate it, and they decide the rules.When this sense of ownership is established, they will participate willingly and with enthusiasm because they will want to be challenged. Teachers must help students tap into and develop their inner authentic selves where they think, feel and care on a deeper level and arouse their interests in learning. In order for students to feel loved and welcomed into their classroom, a community must be built. From this community, students will feel accepted, encouraged and needed in the classroom. When students feel a part of something bigger than themselves, they can accomplish great things and establish lasting relationships.
- Relationship Building: The class works as a team and establishes a trusting support system. The learners work together with each other and the facilitator, and consequently, they don't want to let anyone down. They gain a mutual respect for each other and for the teacher, which descreases discipline problems and increases learning time.
Differentiated Instruction
"Every student can learn, just not on the same day, or the same way."
--George Evans
- Cooperative learning: which provides a sense of belonging for the students. Belonging provides the initial motivation for students to work, and as they achieve academic success, they work even harder.
- Group work: also means no more individual grades as the grades are shared by the team, and where the weaker students are helped by the stronger students.
- Multiple Intelligences: Implementing Gardner's linguistic, logical, spatial, bodily-kinesthetic, musical, interpersonal, and intrapersonal intelligences to enrich students’ learning experiences.This also provides learners with the opportunity to use employ various intelligences and develop their weaker areas.
- Open curriculum: The incorporation of lectures, group discussions, hands-on experiences, video presentations, field trips, reading books, visual materials of any sort, physical performances, presentations, etc.
- Technology Inclusion: Having technology as a resource in the classroom as well as creating lessons that utilize technology.
- Music: Learners can use headphones or I will play music softly.
Learning by Doing
"Education is not the filling of a pail, but the lighting of the fire."
--William Butler Yeats
- It's all about the experience: The late Steve Jobs, an entrepreneur and innovator, was quoted saying: “Creativity is just connecting things. When you ask creative people how they did something, they feel a little guilty because they didn’t really do it, they just saw something. It seemed obvious to them after a while. That’s because they were able to connect experiences they’ve had and synthesize new things. And the reason they were able to do that was that they’ve had more experiences or they have thought more about their experiences than other people. Unfortunately, that’s too rare a commodity. A lot of people in our industry haven’t had very diverse experiences. So they don’t have enough dots to connect, and they end up with very linear solutions without a broad perspective on the problem. The broader one’s understanding of the human experience, the better design we will have.” This design that Jobs is referring to speaks true to the design of 21st century education, where the ability to problem solve, make connections, apply understanding, and reflect in terms of the big picture are qualities instilled within learners. It is the teachers job to provide diverse learning experiences that allow the learners to develop such skills.
- The class must learn to question the traditional assumptions about pedagogy, as right answers are not as important as the process of exploring ideas and understanding the concepts.
- Learning by making connections between old and new experiences is known as the theory of constructivism, generally attributed to Jean Piaget. This theory suggests that learning happens through our experiences and knowledge is internalized through assimilation and accommodation. We experience new information all the time-- reading the newspaper, walking down the street, talking to a stranger at the bus stop, etc.--- and if we are interacting with the world around us, there is no way we can avoid learning experiences. We assimilate these experiences by relating them to old experiences and existing frameworks, or we can accommodate for the new information by reframing our mental representations to fit the new experience. In essence, the learning builds on what we already know and establishes new or more extensive relationships within our mental frameworks.
- This approach works exceptionally well in the mathematics classroom because math is an umbrella of interconnected ideas, so there is an abundance of connections.
- If learners are given the opportunity to interact with others and question new ideas, they will move from the known to unknown.
- Mistakes are celebrated. By accommodating what they thought to be true with what they have found to be true, they are learning from their mistakes and experiences.
- Learning by doing supports The National Council of Teaching Mathematics’ Process Standards- problem solving, communication, connections, reasoning and proof, and representations, and inherently balanced literacy incorporation.
- By using the constructivist approach and NCTM’s process standards as a foundational framework, teachers can focus on giving each learner the opportunity to explore and create their own understanding through differentiated instruction at a level that makes the content meaningful.
- This problem solving process that takes education from a noun to a verb is not only relevant to material in the mathematics classroom, it also relates to problem solving skills needed in real life situations.
- This classroom model encourages learners to make connections and build off of what they already know, and consequently learning occurs much more indirectly, it happens naturally in a meaningful way.
- For this model to be effective, the curriculum can’t hand over knowledge in its final form. The information and experience must be assembled in the learner’s mind in their own way. We must also focus on the teacher-student interaction as well as student-student. Together we can create our own strategies for solving problem situations
- The teacher’s role is essential. They have to set up a structured yet open classroom environment and plan activities that support learners while providing them with choice, and both need to reinforce the learning model.
- The curriculum must be presented to mathematics learners by implementing appropriate conditions for learning: schema activation, focus, activities, and reflection.
- The learning must be relevant and serve a practical purpose. One way to engage the learners is to provide some sort of anticipatory set or schema activation that serves as a connection to their lives. While the opening activity serves a powerful purpose in engaging the learners alone, it must also hone in on the focal point and build off prior knowledge. By opening the lesson in this manner, the learners are encouraged to discuss their ideas with one another and make connections. Most of the knowledge learners build in this stage is from the discussions they have with one another, which is empowering for the learners and gives them a sense of ownership.
- The teacher can direct the discussion by posing questions that scaffold understanding and encourage collaboration. The progression of the discussion should naturally lead the class to the activity, or construction of new knowledge. The activities presented to mathematics learners should be compulsory and have choice. They will allow learners to bring their ideas to the mathematical forefront and explore them using multiple representations. Instead of teaching rules without reason, the teacher will support the learners by asking challenging, open-ended questions that require reasoning and critical thinking skills.
- This method provides the learners with a framework that they can build and expand on to create an individual approach to learning rather than basing their understanding on someone else’s.
Classroom Resources
- Reflective reading strategies must be implemented as they prove to be effective for conceptualization and comprehension. Math can be read similarly to any other language, although, when reading for understanding the context from which mathematics should be read will vary according to each learner.
- To support the diversity amongst learners and how they construct their understanding, the classroom must include access to optimal resources --reading materials, learning manipulatives, calculators, computers, etc.
- The teacher should model how the resources can be effectively and efficiently used to maximize the learning potential in individual and group settings.
- The classroom structure will be free yet organized so the learners can take ownership of their learning by utilizing the resources they have been given.
- The classroom library and resources should be organized and available to learners so they may choose resources that appeal to their interests and accommodate their individual learning levels.
- The goal of this framework is to have each learner working on something they are passionate about, which engages them in the learning process and keeps disciplinary issues minimal.
- To ensure each learner is constructing their own understanding, the teacher must be a large factor in the learning process. That is, the teacher must conference with individuals and groups to discuss the progress and quality of the learning taking place. The teacher can also use this time to assess whether the materials being used match the readiness and interest of each learner and can redirect them appropriately. By facilitating learning in this manner, the learners will continue to be productive as they communicate with one another and build on their understanding.
Motivation
"We don’t get a chance to do that many things, and everyone should be really excellent. Because this is our life."
--Steve Jobs
- Invoke the students’ intrinsic rather than extrinsic motivations to learn. Facilitators can do this by providing meaningful, relevant learning experiences that appeal to the learners' interests, build on their previous understandings, and drive their innate tendencies to want to resolve problems.
- Begin the lesson with a “hook” or “grabber” that engages the learner and drives their curiosity.
- Provide rationale to the learners as to why the particular lesson is worth exploring and how it relates to real life. The rationale should arouse their interest in learning and provide justification for their endeavors and how they connect to their own lives.
- Reduce abstractedness by grounding new learning in the students’ experiences, perceptions and existing knowledge structures so that it feels familiar and comfortable rather than confusing-they have something to relate it to.
- Teach for understanding where students can connect new ideas to other mathematical ideas and to their own lives, which makes the learning applicable and relevant.
- Include learners in the process so they are aware of their own meta-cognitive processes. Encourage them to reflect on their thinking and learning so they, too, can see that they're getting smarter. This will increase their self-confidence and encourage them to continue in their learning.
- Identify relationships among various ideas, concepts, generalizations and facts showing a value for what is being learned.
- Include learners in discussions and decisions regarding their course work and course structure.
- Make the learning relevant by implementing discussions about their education and their careers and why the skills they are developing are necessary.
- As a result, learners will engage in classroom pedagogy because they will see the relevancy of the course work and how it relates to their own lives. Further, they will be intrinsically motivated since they helped develop the course curriculum.