Aly Monson Math Methods

     Through this year-long curriculum, I learned how important it is for teachers to plan ahead. There are so many standards that need to be covered throughout the year and the standards all vary in the length of time it will take to teach and for the students to master. Teachers need to plan for this and read through all the standards at the beginning of the year to make sure they have time to get to everything. I have been in math classes before (more in middle school) that seem to be so rushed at the end of the year which could have been due to the teacher’s lack of a year-long curriculum plan. Obviously, other things could have come up or lessons took longer than my teacher thought, but it still reminds me of the importance of having a plan because I know how stressed I was when I had to learn concepts too quickly and didn't have time to master them before the tests. I also learned how important it is to review standards from the previous grade because they tie in so...

  Based on the seven pieces of student work on the gumball problem, I learned that this problem shouldn't be assessed or graded as just right or wrong. To properly assess student learning or student knowledge using this problem, teachers need to understand the student’s thinking. If they got the right answer, teachers need to determine if the student actually understood what the problem was asking and how to use probability to get that answer, or if they just guessed. That is important in this problem specifically, because the problem basically asked the student to give an answer that was an integer between 1 and 10 and the correct answers were 4-6 so if a student guessed, they still had a 30% chance of getting it right even without understanding the problem or the concept of probability. If the student got the wrong answer, it is also important to understand the student’s thinking. Some of the students got the wrong answer because they really didn't understand probability. Som...

       I read the article “Facilitating Student-Created Math Walks” written by Min Wang, Candace Walkington, and Koshi Dhimgra and published in the September 2021 issue of Mathematics Teacher: Learning and Teaching PK-12 . Before reading this article I had never heard of the concept of a math walk. A math walk allows students to get outside the classroom and find math in everyday life. After reading this, I realized that I have done something similar to a math walk in my high school geometry class when we were given a list of geometric shapes and angles and we has to walk around the school and take pictures of them. The article explains the five steps teachers can follow to design each stop in a math walk. The first step is to observe the space, then pose questions to the students to get them thinking and allow them to ask questions, then connect those questions to STE(A)M fields to help the students connect it to outside mathematics. After all the stops are planned ...

   Posing purposeful questions reminds me of the third CCSSM Standard which is Construct viable arguments and critique the reasoning of others because teachers should pose purposeful questions to gauge student understanding and students communicate their understanding back to the teacher through their arguments of why they got the solution they did. There are five types of purposeful questions teachers ask students which are all used for different purposes. The first type of purposeful question is gathering information, which teachers use when want students to recall basic facts or definitions (mostly things that are memorization). This is a question used to assess students because it usually has a right and wrong answer and can help the teacher gauge whether or not the student understands. The second type of purposeful question is probing thinking, which is used when teachers want students to explain, elaborate, or clarify their thinking and reasoning and why they came up wit...

A conceptual understanding of math is essential for students to be successful in math classes throughout their life. To me, conceptual understanding is the basics of math (addition, subtraction, multiplication, division, equalities, etc), why these concepts work, how they work together, and then being able to remember and draw from these concepts in more complex problems. In order for students to gather conceptual understanding, they need to be willing and ready to learn and they also need to believe in themselves and their intelligence. The teacher's role is to be the expert but to guide students toward these understandings and not simply state them like facts, or else students will memorize them and not understand why these concepts work and why they are important in the future.  Procedural fluency is the ability to use equations, representations, manipulatives, etc to solve a simple problem. The word simple is relative to the child’s grade level and also their academic level. Fo...

  https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Grouping-and-Grazing/   For my first Math Applet Review, I chose the Illuminations (NCTM) website and quickly realized there are way too many activities to review in one blog post so I will be specifically focusing on the game called Grouping and Grazing. This game is designed for PreK through 2nd grade and works best on tablets and laptops. The student’s objective of the game is to help the alien spaceship move cows into corrals by counting, adding, or subtracting. This activity helps children learn grouping, tally marks, and place value. As they master counting, they can move on to adding and subtracting two-digit numbers. One thing I really like about this game is it can be used for students who are working on counting by 5s and 10s and then can be differentiated for students working on addition, then subtraction with a simple click of a drop-down menu. I want to teach special education and I will have a ...

          The Common Core Standard of Mathematical Practice that I researched was Standard 2: Reason Abstractly and Quantitatively. My partner and I learned that standard 2 involves students decontextualizing and contextualizing problems to help make sense of them to solve them. Decontextualizing involves taking a complex problem and representing it with symbols that are easier to understand. An example of this would be a student drawing a picture of a word problem and then being able to make a number sentence or equation that they are able to solve. Contextualizing involves taking a problem that is numbers or symbols and putting them into a real-world situation (often a word problem) to help students understand how to solve the problem. To help young students develop this skill, teachers need to help students learn the relationships between numbers (greater than, less than, or equal to) and also teach students how to do basic addition, subtractio...