Reflection Chapter 4
In my work at Conestoga Middle, our teachers are using a constructivist math curriculum, Connected Math. Constructivism promotes instructional strategies focused on student’s thinking and deep conceptual understanding of the material presented. Teachers can increase their understanding of student’s understanding by listening to student discourse and giving students challenging problems that require them to share mathematical thinking and justifications. One needed practice in classrooms today is the development of classroom cultures that promotes mathematical inquiry. With the use of protocols, all student voices can be heard. Teachers must promote equitable practices that allow all students entry levels into the classroom work. Within classrooms, students need to collaborate with peers as they discuss and discover the math within the problem solving tasks. Teachers need to access prior knowledge of students, which can be used as a starting place for instruction and provide scaffolding of lessons that lead to higher student achievement. Students should have ownership of their activities during the learning process and share in the presentation of ideas and mathematical reasoning behind their work. Presenting students with rich mathematical tasks can press students’ thinking and lead them to discover generalizations. Students are asked to share math reasoning through multiple lenses such as graphs, tables, and equations. Multiple representations of solutions lead students to deeper understanding of the mathematics, and validate individual differences of thinking. Teachers need to teach critical thinking skills that are used in the problem solving process. Some strategies include making and confirming conjectures, questioning, visualizing, summarizing, drawing inferences, use of authentic situations, synthesizing, analyzing, generalizing, evaluating, and self-reflection. Document cameras and graphing calculators used within classroom allow students to make math presentations of their authentic work. Constructivism allows teachers to use rigorous and relevant mathematical problems. Important relationships between students, parents, and teachers are needed for this process to have the greatest gains.
Gardner’s work around the concepts of multiple intelligences is very useful in preparation of lessons and teaching. The logical-mathematical intelligence is found within mathematicians, scientists, accountants, and many other career paths that involve the ability to compute and apply higher math concepts to everyday life. One activity that appeals to learners with this strength could be finding the breaking weight of bridges in relationship to the thickness of bridges. An extension could include looking at bridge structures to identify angles of construction within the bridge that would support the greatest weight. Students could start with paper bridges, compare thicknesses using pennies as weights, and then move into construction of bridges with toothpicks to compare strengths of bridges based on the construction of the supports. Students actually are able to test the strength of their bridges once constructed. Other activities might include the basic understandings of interest and application to savings accounts. Many ideas and lessons support the development of student’s learning with this intelligence.
Linguistic learners often are journalists, writers, poets, lawyers, and many other areas that involve the ability to use language to describe and express ideas in writing. As I think of math and how I could promote student’s learning with this intelligence, I think of journal writing ideas and reflections around the math content they are currently using to help inform a teacher’s knowledge of their progress. Last year, I used a persuasive essay assignment asking students to develop an argument of whether females or males were better mathematicians. The students had to research the topic and give evidence of their choice. It was fun to watch the students try to persuade their peers of their choice and reasons.
Musical intelligences are found within musicians, composers, and anyone with the ability to understand and develop music. Students with these abilities are extremely detail-oriented and analytical. In math, this is seen within areas that require justification and explanations of work. Math is found within music lessons as student’s study notes and their counts. When students study Pythagoras, they will find that he was one of the first mathematicians to connect music to math. Fractions are involved in music notation of guitar strings. Each string was 1/5 of a whole. I have also had students make rap lessons to help them remember certain math ideas that required multiple steps.
Spatial learners have the ability to visualize and often, use diagrams or tables to share work. In math, students with this strength do well with geometry lessons. Drawing 3-D images and being able to break them down to form nets to find surface area is one activity that pops in my mind. Another is using tables and graphs to be able to find the slope of lines.
Interpersonal learners have the ability to have personal insight and understandings. These learners are social. They love the collaborative group process. Lessons using rich problem solving tasks are great for students with this strength. The interaction with others is key and these learners keep the group progressing by inviting thoughts from all students within the group. The intrapersonal learner is the opposite. These learners are reflective. They are quiet, but are thinking through the process silently. They are great at the reflecting process within groups and helping others summarize what they have done. These learners are often the ones who arrive at the generalizations in math lessons first.
Students who are bodily-kinesthetic learners are often your athletes, dancers, surgeons, sculptors, and anyone who has the ability to use parts of the body to excel. These students learn best by moving and practicing content through hands-on activities. One math lesson I have used to support these learners is using hopscotch to learn order of operations. Students chant the order as they jump. Another idea is to have student act out geometric shapes using their arms and body. I have students demonstrate circumference of a circle by putting an imaginary belt around their waist. There are many activities to engage kinesthetic learners in math.