I truly believe that math is at the center of all learning. We use math in our every day lives without ever thinking about it. It is so crucial to illustrate to students the importance of math and how math can be applied to real world situations and problems. I have always loved mathematics and numbers, and I know a lot of students struggle with math and believe they can't do it or they aren't good at math. As an educator, it is vital to acknowledge to students that math can be difficult and it takes time and practice to master certain skills. Students need to be encouraged to take risks and be reminded that mistakes are okay and they allow students to learn and grow even more. Using language like scholars and mathematicians will help students get into the mindset that they have the ability to do math. Students should be encouraged to think critically, try to the best of their abilities, keep trying and preserve, ask questions, justify reasoning, and above all be open-minded. Mathematics is more about understanding than getting all answers correct. Calculators can compute all sorts of numbers, but it doesn't understand why. Students need to focus more on understanding the material in mathematics, rather than stressing about doing poorly because their final answer was wrong. Math should be taught to students using a variety of different strategies and tools so all different types of learners can successfully learn. Project-based learning is a great way to get students critically thinking, doing research, and connecting math to real world problems. Math should be hands-on and interactive for students to get them engaged as much as possible in the lessons. The beauty of mathematics is that is builds upon itself to reach advance levels. As an educator, it is important to build a strong foundation in mathematics for students to set them on a successful path in whatever career they choose. I love math, and I hope to instill that same enthusiasm and love into my future students!

The Gradual Release of Responsibility Model is a teaching strategy that focuses on releasing the responsibility of learning to students in a process of four steps. The four steps are I do it, we do it, you do it together, and you do it alone. As the lesson progresses, the responsibility of the teacher decreases and the responsibility of the student increases. The purpose of this model is to move students towards independence.

Focus Lesson (I do it):

The focus lesson or instruction is the first step of the Gradual Release Model where teachers hold all of the responsibility. In this section of the lesson, the teacher will introduce the lesson and preview what students are going to be learning about. The teacher will go over explicit behavioral expectations with students. This is also the time where the teacher will explain the learning objectives and essential questions. The teacher will model for students the mathematical concept(s) being taught and walk through how the teacher would answer the question or work through a problem. The teacher provides an example for students before they have to try it in group work and independently.

Guided Instruction (We do it):

The guided instruction is the second step of the Gradual Release Model where teachers hold most of the responsibility, but is giving a portion to students. In this section of the lesson, the teacher will provide students with additional examples to try as a class. The teacher will still continue to guide students and scaffold questions to help students work through the problem when needed. The teacher will call on different students to help solve the problem as a class. This could also be where the teacher asks students to turn and talk to discuss their questions or ideas.

Collaborative (You do it together):

The collaborative part of the lesson is the third step of the Gradual Release Model where teachers transfer the majority of responsibility to students, but still keeping some to help students and push them in the right direction or answer any questions. In this section of the lesson, students are partnered together or put in small groups to work on a few problems on their own. The teacher will walk around to informally assess students and help where ever is needed. Students will have to collaborate and work with peers to help one another solve the problems that were given. The teacher will then have students come back as a class to discuss what different students' got as an answer or how students' problem solved and the method or strategy used. This is also the time students could ask any questions to get clarification before moving on in the lesson.

Independent (You do it alone):

The independent part of the lesson is the fourth step of the Gradual Release Model where teachers transfer all of the responsibility to students to work independently. The students will most likely turn in their work as a form of a formal formative assessment for the teacher to analyze to see which part of the lesson went well and which part needs clarification. Students will work with similar problems from the lesson to apply and practice their skills on their own. Students can ask the teacher if they have any questions to get clarification. This will demonstrate to the teacher if students understood the material covered in the lesson.

The teaching instruction of procedural and conceptual understanding is very different, but in order to have a balanced class, especially in mathematics, it is important to have a mix of both understandings in the classroom.

Procedural understanding is focused on the use of math rules, procedures, and algorithms. This instruction relies heavily on mathematical language and symbolic representations. Procedural understanding is learned through memorization and practicing math skills over and over until they become automatic. The problem with just using this type of instruction is that students won't understand why and what they are doing, and just simply memorize the material being taught. This makes it much more difficult to apply those math skills in different situations and real world applications. Procedural understanding should always come after conceptual understanding in terms of instruction.

Conceptual understanding is focused on making a network of connections to math ideas and understanding their meaning. This instruction relies heavily on building mathematical relationships between different concepts or topics in math, as well as understanding how and why math is solved in certain ways and the methods used. This will help students make connections to multiple topics in math and understand how to apply their knowledge and skills to different situations and real world applications. In this teaching instruction, students are actively reflecting and processing the math material being taught to foster an understanding of what they are learning. Since math concepts build upon each other, it is important to set a strong foundation of conceptual understanding for students. Conceptual understanding should always come before procedural understanding in terms of instruction.

A major difference between accommodations and modifications is that accommodations are made to help different types of learners or students with disabilities learn the same material as their peers, just in a different way. Modifications are made for different types of learners or students with disabilities to change the material and what the students are learning. Both accommodations and modifications are written in IEPs or 504 Plans for students.