Table Of Contents
Math Education Philosophy
A child development theorist that inspires me in all realms of teaching is Lev Vygotsky.
Lev Vygotsky created the Zone of Proximal Development Model. This model states that there are three zones of development. A zone where the student is, a zone where the student can be with instruction, and a zone where the students can't yet reach. The role of a teacher is to bring the student into that area where students can learn with instruction. Overall this model has taught me that teaching is about reaching a child where they are and scaffolding instruction until they are where they need to be.
It is our job as math teachers to ensure that students do not develop an aversion toward the subject. We can do so by scaffolding instruction so that math problems are at an instructional level of teaching rather than a frustrational level. We need to make math work engaging and enjoyable. We need to make sure that students are not afraid to make mistakes in math mindset, and most importantly we need to teach our students to have a growth mindset when it comes to math.
It is important that all students participate in math class. When students are engaged with the math materials, they can learn more effectively. As math teachers it is necessary that we make our math lessons engaging. It is also necessary that we make sure all students are participate and can participate in math lessons. It may be intimidating for some students to participate in math lessons, but we can diminish this anxiety by utilizing the think, pair, and share technique and by scaffolding problems effectively.
The Gradual Release Model is an instructional model that slowly transfers the responsibility of learning from the teacher to the individual student.
When using the Gradual Release Model you can use four steps:
First, you will explicitly teach the class the material
Then, you will have the class collaboratively work on math problems
Next, you will have the students solve problems in small groups
Finally, you will have students work on math problems individually
Math centers may sound like an intimidating concept to new educators, but if they are used effectively, they can be a great tool for learning. A math teacher should make sure that students are arranged in groups based on assessment scores and classroom demeanor. By assorting students into particular groups, the teacher can ensure that students receive targeted instruction for their skill level. It can also help students get used to working with peers in small groups
Overall, assessments inform adjustment to practice. It is best for teachers to find where their students are and how to best teach them.
(a) Essential inquiry question
When assessing your students make sure to assess them on your essential inquiry question. This way, assessments ensure that you effectively taught and addressed the essential inquiry question in your math instruction. It also informs you on whether students understood the essential inquiry lesson in the instruction.
(b) scaffolding questions
There will always be diverse learners in your classroom. It may be necessary to scaffold some questions on your math assessments to ensure that all students are being tested equitably.
(c) Higher-level thinking questions.
It is also necessary to include higher-level thinking questions on your math assignments. An important quality of strong math instruction is challenging your students and having high expectations. Some problems should be rigorous so that students require persistence. This will help students become more effective mathematicians. Some students may also be advanced in math, these questions will add some rigor to math assessments
Formative assessment in math education is the ongoing assessment of student progress throughout a math unit. This can include worksheets given during the unit, as well as visual and verbal assessments of the students throughout daily lessons. An effective teacher will use ongoing formative assessment to ensure that students are meeting unit objectives. Formative assessment can inform a teacher on how to proceed during a lesson. It can also inform teachers on how to adjust practice in upcoming lessons.
A summative assessment is an assessment given at the end of a unit to measure the students learning. This assessment can be compared to the unit preassessment in order to effectively measure how much the students learned throughout the unit. A summative assessment will assess the unit goals presented throughout the unit and if any adjustment to practice is needed for future units.
Algorithmic Problem Solving
It is not justifiable to rely solely upon the algorithmic problem-solving methodology. Typical algorithmic problem-solving is often based on abstract concepts. In order for students to understand math effectively it is important to make sure to students have a conceptual understanding of math concepts. For example, if you are to teach a student that 3x3 means three groups of three and you show the student this in a visual manner, the students can develop a more concrete idea of 3x3 than if you just had the students remember that it is equivalent to nine. Math is also cumulative in nature so learning can be very difficult and frustrating for students if they do not understand foundational math skills.
These are three different ways that teachers adjust their lessons to meet their students educational needs
Accommodation- "A change to instructional or testing procedures or materials that allows a student to fully access the information and to accurately demonstrate knowledge" (IRIS Center, 2022)
It is important to remember that an accommodation does not change the content of instruction, change the expectations for learning, or reduce the requirements of a task
Examples of accommodations
Materials in Braille
Graphic organizers
Extended time on tests
(IRIS Center, 2022)
Modification- "A change to the instruction or curriculum that alters either the content of that instruction or student performance expectations. Modifications are for students who need more intensive assistance than accommodations can provide" (IRIS Center, 2022)
It is important to remember that modifications do not change the expectation for learning or reduce the requirements of the learning task
Examples of modifications are
Reduced assignments
Different reading materials
Test on a smaller set of the content
(IRIS Center, 2022)
Learn more - https://iris.peabody.vanderbilt.edu/
Universal Design for Learning-
"Universal Design for Learning (UDL) gives all students an equal opportunity to succeed. This approach to teaching and learning offers flexibility in the ways students access material and show what they know. UDL also looks for different ways to keep students motivated" (Morin, 2022)
Summarize how your approach to teaching math considers English Language Learners. How do you ensure you address a variety of English proficiencies and variety in cultures?
When teaching English Language Learners math, it is necessary to scaffold lessons to meet the students where they are. ELLs are at a variety of English Proficiencies and it is necessary to take into consideration the individual needs of each student when creating lesson plans. One way that we can adjust our math lessons to be more accessible to ELLs is by using visuals and by teaching math visually. It is also necessary to make sure that the students have access to manipulatives so that the students can learn math through tactile experiences. In math instruction, I will also make sure that all students in my class see themselves represented in math instruction. There is a large variety in cultures I will learn everything that I can about my students so that they feel seen in math.
Morin, A. (2022, September 15). What is Universal Design for learning? Understood. Retrieved December 19, 2022, from https://www.understood.org/en/articles/universal-design-for-learning-what-it-is-and-how-it-works
Accommodations versus modifications EST.. time: 30 Minutes. (n.d.). Retrieved December 16, 2022, from https://iris.peabody.vanderbilt.edu/wp-content/uploads/pdf_activities/independent/IA_Accommodations_versus_Modifications.pdf
Mcleod, S. (n.d.). Lev Vygotsky's sociocultural theory. Lev Vygotsky's Sociocultural Theory - Simply Psychology. Retrieved December 19, 2022, from https://www.simplypsychology.org/vygotsky.html