Classrooms, schools and neighborhoods today are typically extremely diverse with a variety of ethnicities and backgrounds thrown together. Students need to be able to work with a variety of different people and those who may not have the same beliefs as their own in both school and in their own neighborhoods. To help prepare the students for this, group work and cooperative learning becomes extremely important in a classroom. Students should be placed into groups in which they will be expected to cooperate and accomplish set goals with other students that may be of different ethnicity, race, sex, or cultural background. Cooperative learning is also very important because it allows students to learn with the help of others in their groups. Vygotsky proposed that thinking is social and therefore thinking is advanced and enhanced through social interaction such as group work and cooperative learning. This is especially true for mathematics. Students normally have a difficult time picking up topics that are not just solving a problem using an equation or where more mathematical logic is needed to solve the problems. Working with their peers on problems that they have difficulty with allows them to talk out solutions with someone and provides greater understanding of the concept then they would have had if a teacher had given them the answer or shown them how to complete the problem. Uri Treisman also completed research into using peer groups to enhance student’s achievement rates in higher level math classes. He found that students were not lacking in motivation or academic skills, but rather the students had patterns of studying by themselves, which was putting them at a disadvantage. Treisman found that putting the students in groups in which they would study and complete certain tasks together greatly increased the student’s progress and achievement in the class. Mathematics is not a topic in which isolation increases a student’s understanding, but rather acts as a disadvantage. Highly structured cooperative learning activities with clear goals helps student collaboration that greatly enhances their understanding of the concept.

Mathematics is an interesting topic that can be seen throughout someone’s daily life and this should be instilled in students. Students who say that they do not like math typically follow this up by saying that they don’t understand why they have to learn something that they will never use. Students use mathematics constantly; from figuring out how much a new laptop is going to cost them with tax included or how much they are spending on gas to get from point A to point B. The real-world applications of math should be a daily part of the lessons teachers provide students. These applications can go from simple calculations of how much a discounted blouse is at the mall to basic descriptions of how engineers use these same calculations to compute the amount of concrete needed to build a bridge. Students need these skills in their everyday lives, and at this point in their lives many of them are trying to find a career that speaks to them. Teacher should be able to show them the possibilities and explain to them how having a general idea of such things can save them from getting taken for a ride by some contractor. Bronfenbrenner said that a developing child is embedded in a series of complex and interactive systems. He went on to say that to understand human development it’s important to consider the entire ecological system in which growth occurs. It is important to show the students how what they are learning in their math class is connected to all the other systems that they are interacting with. This will make mathematics more accessible to the students and therefore more interesting.

Every person’s fingerprints are different. Every person’s DNA is unique. Why would every person have the same way of learning that is best for them? They don’t; every student has a different way in which they learn the best, therefore teachers should provide differentiated learning opportunities to their students. This goes along with the previous topics discussed in my educational philosophy. Students should be given a variety of ways in which to grasp a concept. When a teacher differentiates his or her instruction, they are giving the students more strategies for acquiring and using information. Siegler, one of the main information processing theorists, noted that a teacher’s instruction may be limiting strategies that students can use. His research showed that a student’s large variety of problem-solving and memory strategies can account for the differences in performance between different students. Students who have more attuned metacognition skills are generally more prepared to do well not just in math, but in all subjects in school. By differentiating instruction, a teacher gives students a wide variety of strategies, and teaches effective strategy use thus promoting advanced development. Howard Gardner’s research also supports the idea of teachers being flexible to their approach to teaching and adjusting their curriculum and presentation of material to students instead of expecting students to modify themselves. Gardner’s theory of multiple intelligences provides a premise behind the idea that there are different ways of being "smart". He has identified eight different types of intelligence including logical-mathematical, linguistic, visual-spatial, body-kinesthetic, musical, interpersonal, intrapersonal, and naturalistic. While traditional methods of teaching reach only two of these intelligences, by differentiating instruction a teacher can attempt to weave all eight intelligences into their teaching, giving students more chances to understand what the information the teacher is trying to give them.