Math is one of the areas that I feel is so important to communicate with parents about because of the different methods that we introduce and because parents see it daily through homework. It's one of those tangible things they can try to understand about what their child is learning in school. And for that reason, I think it stirs up a lot of concerns, questions, opinions, and ultimately, a desire to help.{I have a secret strategy for math homework that is perhaps a little sneaky--I don't send homework on a concept until students have had ample time to play with it in math class. This means that homework is usually a week behind my instruction. Still, parent questions often arise from math homework}.
We know, it's called "New Math" and parents can sometimes push against that, but a lot of the way I teach math was also new to me (and I'm a stubborn beast when it comes to change sometimes). I loved math when I was in school and was good at it. All those old methods worked for me too, but I see merit in our "new methods" which are really conceptual models for understanding math procedures.
We know, it's called "New Math" and parents can sometimes push against that, but a lot of the way I teach math was also new to me (and I'm a stubborn beast when it comes to change sometimes). I loved math when I was in school and was good at it. All those old methods worked for me too, but I see merit in our "new methods" which are really conceptual models for understanding math procedures.
Anywhooo, although I think communicating about math is extremely important, this year, I haven't been doing a good job of taking the time and sharing information with parents on the classroom blog. In a perfect storm with the new year, it was time for our mid-year reviews of our individual growth plans. I decided to change one of my individual growth goals to increase my focus on parent communication related to math instruction {committing to posting once a week about math}. I have been doing a little research here and there and firing away blog posts about how I think about and organize my math instruction, how I differentiate, and how parents can help with homework. I am also working on explanations of how I taught multiplication and division--I'm a little behind, but I see this being so helpful next year when I already have some posts ready to go. The "Levels of Understanding" post is my favorite. Take a look below!
Introducing: Math Spotlights!
One of my goals for the New Year is to share more information with you all about math instruction. I hope to share the methods students are learning, details about our math class routines, and examples of below-, on-, and above-grade level expectations. This post will serve as an overview of our math routines and my approach to math.
What does math look like in our classroom?
What does math look like in our classroom?
- A typical week in 4th grade math includes 2-3 days ofstations with students completing activities at different levels of difficulty. Students may be working independentlyor in a guided group with me, Mrs. Morris (our teaching assistant), or Mrs. Kuhl (our AIG teacher). In stations, students solve computation problems where we focus on being more accurate and making sure we understand the steps to different methods. Students also have stations where they review concepts, work with word problems, and use dreambox.
- 1-2 days a week, I introduce new concepts while reviewing old concepts. For example, in the upcoming week, I will be introducing fractions concepts with some picture and number sorts (to gauge students current understanding of fractions). In addition, we will spend half of our math timereviewing and extending our understanding of how to divide larger numbers.
- On Fridays, students complete some form of assessment. This may be review questions from concepts we learned earlier in the year or directly related to what we are currently studying. Often, this information is used to create leveled groups in stations for the following week. The difference between regular math days and "assessment Fridays" is the level of support that I am willing to give students. On assessment Friday assignments, I offer as little support as possible and really try to encourage students to show what they know. When I offer support to help a student get the answer, I write directly on their paper and/or initial it so that I know they did not complete the problem independently.
Math Spotlight: Helping with Homework
I have chosen to use spiraled math homework that covers many concepts instead of homework that only focuses on the concept that we are learning on a given day. This means that your child will see concepts that they have learned months ago, weeks ago, and possibly even concepts that are coming up. While I believe that this type of homework is really beneficial for me (and the child) as I hope to keep students' previous learning sharp, assess their ability to independently complete concepts we are currently focusing on, and see who can solve problem-types that I have not yet discussed, I know this may also be a source of confusion and frustration at times. How do you know what your child should have mastered already? (I'll address more about this in an upcoming post). And, most importantly, how do you help?Can you help your child with math homework? Absolutely! It seems that resisting a parent's help with math homework is a typical "coming of age" behavior for 4th and 5th grade students. However, many of you feel that it is an important role for you to play in your child's education and I would agree. Read more here...
Math Spotlight: Levels of Understanding
Typically, before introducing students to the traditional way of solving math problems, I use manipulatives (ones cubes, tens sticks, hundreds blocks, etc) or printed models (pictures) to help students think about and understand what the computation really means. Using hands-on activities and guiding students through different types of questions helps me assess the depth of their understanding. My goal is not to simply teach students to memorize steps and procedures, but to ensure that they understand why they are doing what they are doing in each step.
When we think about learning skills and concepts, we should imagine those skills and concepts on a continuum of learning with children at different levels of readiness. Given a specific concept, your child may be at different levels at different times. I found the following descriptors from Kathy Richardson (she's a math guru that develops materials for assessing students' true understanding and misconceptions):
Ready to Apply (A) – The student can already do a particular task and is ready to use this skill in other settings. (This student receives more challenging work).
Needs Practice (P) – The student can do a particular task with some level of effort but still needs more experiences to develop facility and consistency. (This student typically receives work at grade level that increases in difficulty as his/her readiness increases.)
Needs Instruction (I) – The student has some idea of what a task is about but needs support. (This student receives direct instruction that begins with the lowest level of their individual understanding and builds up to problems with increased difficulty to help meet grade-level expectations.)
Needs Prerequisite (N) – The student does not yet understand the concept and needs to work with mathematical ideas that precede the concept being assessed.
When I discovered these descriptors, I really wanted to jump up and down--I was excited because these categories of learning really capture how I think about individual students' understanding of a math concept and how I choose materials and create groups for focused instruction.
It is also important to consider the size of the number(s) when placing students at these levels for a given concept--the size of the number with which they are independently successful needs to be taken into consideration. I often find that concepts that students may seem to have "mastered" are merely in the process of truly being understood when they are presented with larger numbers. As we know, accuracy also becomes a larger issue as the size of numbers increase. To instruct students having difficulty (say learning the procedures for how to multiply 23 x 67), I begin by taking a step back and instructing them on how we would solve a simpler problem, like 23 x 7. Once the student has consistently demonstrated that they are able to complete problems at this level, we move on to adding a digit in the tens place for the second factor.
Next up...
I'm going to share examples of problems that are below, on, and above grade level based on NC state standards for math. When you see your child's math work, you can use these levels to have a better understanding of what they have accomplished. If they are successfully completing below and on grade level problems, but having difficulty with above grade level, this means that they are where they are supposed to be and that they are being challenged to push beyond the average 4th grade expectations. If they are having difficulty with "on grade level" problems, rest-assured that they are being served in a small group that meets them where they are and works to help them build up to solid grade-level abilities.
When we think about learning skills and concepts, we should imagine those skills and concepts on a continuum of learning with children at different levels of readiness. Given a specific concept, your child may be at different levels at different times. I found the following descriptors from Kathy Richardson (she's a math guru that develops materials for assessing students' true understanding and misconceptions):
Ready to Apply (A) – The student can already do a particular task and is ready to use this skill in other settings. (This student receives more challenging work).
Needs Practice (P) – The student can do a particular task with some level of effort but still needs more experiences to develop facility and consistency. (This student typically receives work at grade level that increases in difficulty as his/her readiness increases.)
Needs Instruction (I) – The student has some idea of what a task is about but needs support. (This student receives direct instruction that begins with the lowest level of their individual understanding and builds up to problems with increased difficulty to help meet grade-level expectations.)
Needs Prerequisite (N) – The student does not yet understand the concept and needs to work with mathematical ideas that precede the concept being assessed.
When I discovered these descriptors, I really wanted to jump up and down--I was excited because these categories of learning really capture how I think about individual students' understanding of a math concept and how I choose materials and create groups for focused instruction.
It is also important to consider the size of the number(s) when placing students at these levels for a given concept--the size of the number with which they are independently successful needs to be taken into consideration. I often find that concepts that students may seem to have "mastered" are merely in the process of truly being understood when they are presented with larger numbers. As we know, accuracy also becomes a larger issue as the size of numbers increase. To instruct students having difficulty (say learning the procedures for how to multiply 23 x 67), I begin by taking a step back and instructing them on how we would solve a simpler problem, like 23 x 7. Once the student has consistently demonstrated that they are able to complete problems at this level, we move on to adding a digit in the tens place for the second factor.
Next up...
I'm going to share examples of problems that are below, on, and above grade level based on NC state standards for math. When you see your child's math work, you can use these levels to have a better understanding of what they have accomplished. If they are successfully completing below and on grade level problems, but having difficulty with above grade level, this means that they are where they are supposed to be and that they are being challenged to push beyond the average 4th grade expectations. If they are having difficulty with "on grade level" problems, rest-assured that they are being served in a small group that meets them where they are and works to help them build up to solid grade-level abilities.
I have a few things in the works for math that I am super-excited about, including an upcoming giveaway that you won't want to miss...we are on our 3rd snow day and I have been using this time to work away on a few things I have been wanting to create. Thanks for stopping by and stay tuned!
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