We are a Growth Mindset Classroom

What is a growth mindset? 

A person with a growth mindset believes that abilities can be developed through commitment and hard work. 

This is different from a fixed mindset belief that our basic qualities (our intelligence and talents) are fixed traits that cannot be changed. 

Research has shown that people who believe they can learn, who recognize that hard work pays off, and that minor setbacks lead to more growth  can actually rewire their brains! 

Our 10 Growth Mindset Beliefs

1. I can learn anything because I was born to learn.

2. I can train my brain through practice.

3. I can choose my thoughts when things are hard.

4. I know failure is an important part of success.

5. I take ownership of my mistakes and learn from them.

6. I do not let setbacks keep me from accomplishing goals.

7. I believe that I can do hard things.

8. I take charge of my own learning. 

9. I encourage others to have a growth mindset.

10. I celebrate my own growth progress. 

Although we will be wrapping up our Growth Mindset Lessons this week, the classroom environment provides the perfect setting for continuing to discuss these beliefs. When math gets challenging or we have to push ourselves to revise our stories in writing, we will remind ourselves of how growth minded people respond to challenges!

~Mrs. Roose

* Credits: I am using Growth Mindset Materials written by Angela Watson. 

Math Spotlight: Multiplication of Larger Numbers

During 2nd quarter, we learned multiplication of larger numbers with a focus on different methods that can be used. In this post, my goal is to share with you how I have taught different multiplication methods so that you will have a better awareness of the ways you may see your child completing math problems and to provide you with a greater understanding of grade-level expectations. Students may also use this post to help themselves recall what was discussed in class.

Math Vocabulary: How do we talk about multiplication?

 

factor: the numbers being multiplied together
product: the result of multiplying numbers (the answer)
divisor: the number doing the dividing; the number going into the
dividend: the number being divided;
quotient: the result of dividing the dividend by the divisor (the answer)

What does below, on, and above grade level expectations look like for multiplication? I have decided to call these three levels of mastery "Building Blocks," "Goals," and "Gold." These levels are marked with dot symbols (2 dots, 3 dots, and 4 dots) Take note of the 3rd grade standard "Know from memory all products of two 1 digit numbers." I was surprised to see this directly stated in 3rd grade standards. Many of us are still working on multiplication fact mastery, but this made me feel that it is even more critical for students to leave 4th grade with solid recall of multiplication facts. 

Two Methods for Multiplication:

As we work with larger numbers, we use the rectangle method and the traditional method.


Rectangle method- This method splits the factors into place value parts (ones, tens, hundreds) and uses a rectangle to represent splitting the numbers apart. A two digit number would be split into two parts (tens and ones) and therefore needs two boxes. When you multiply a two digit by a two digit, you end up with four boxes. Notice how this looks like an rectangular area problem---you now multiply the “length” and “width” to find the partial products (or partial answer). You add all the parts to get the final product. (Recall that you also have to add in the “standard” multiplication method.)




= 740


+

= 148

= 888


With the rectangle method, students can visualize the idea that all parts of one number multiply all parts of the other number. The key here is that students understand you do not just multiply the tens in each factor and the ones in each factor (this is a common misconception), but the tens AND ones in each number must multiply the tens AND ones in the other number. So, a student who misconceives multiplication would think “I multiply 20 x 30 and 4 x 7. Add those together and I am finished.” (Nope!!!)

Shortcut/Standard Method: This method is how most of us were taught to multiply. The issue with going straight to this method is that it often creates students who don’t really understand multiplication, but know how to follow the steps. At this age, we are lucky we have the time to ensure students understand what they are doing. Common misconceptions/mistakes with the standard method include not shifting the second line over (which you do because when you multiply 2 x 7, you are really multiplying 20 x 7, therefore need to shift the second partial products over.) Often students are taught to “put a magic zero there” but don’t always know why they are doing so. I resist calling it a magic zero and always try to explain "It's because you are really multiplying by a ten." Note that being able to follow the standard algorithm is actually a 5th grade expectation, but I have taught it for mastery this year.

I know this post is packed with info, but I hope you enjoyed taking a closer look at the multiplication standards and methods we used in class. Eventually, I would like to start sending home skills traces like the one pictured above so that you have concrete information about grade level expectations. I am working to build assessments based off of these skill levels where a student knows he/she is moving through "Building Blocks," "Goal," and "Gold" type questions. Look for these in the future!

How does this connect to homework? You will see some above grade level (gold) questions on homework. This is because many students are ready for taking it to the next level and "gold" questions provide enough challenge to maintain a rigorous curriculum for all children. Now that you know what "GOALs" 4th graders have, you should expect that your child can solve those problems accurately and independently. I may even be able note the levels on homework now by using the 2, 3, and 4 dot system! How exciting!

Math Spotlight: Levels of Understanding

This week's post focuses on "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. 

By the way, I'm ready to reveal a secret...I'm a bit of a "math nerd" and I think that's cool!

Math Spotlight: Helping with Homework

How Can You Help with Math Homework?
I have recently had conversations with a few parents about math homework and would like to spend some time addressing math homework routines at home and school.

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. Looking over your child's math homework is definitely a way to keep yourself in the loop of how they are progressing and what the expectations are for 4th grade math.

Often, resistance comes from parents showing the child how to solve the problem using a different method than what was taught in the classroom. This can be confusing for a child when they are having difficulty understanding (or remembering) the method the teacher is using in class; however, for a child who has a good grasp on one method, introducing another method can help develop their math understanding. I often think we--students, teachers, parents--are looking for the "easier way" to solve math problems, but the truth is the only "easy" way to multiply or divide large numbers is to use a calculator! :) Regardless of the method students are taught or choose to use, learning how to do something new takes time. I teach at least two methods for solving multiplication and division problems because it allows students to develop deeper understanding and it gives them an additional way to check their work. Developing flexibility with different methods is also an expectation of our math curriculum.

It is truly my goal to do a better job of helping you help your child in the upcoming months. I will share videos that show the methods I have taught for multiplication, division, and other concepts. I will also share videos that can be used to help your child independently review concepts and additional websites that they can use to practice.

How do I use Math Homework?

Each morning, math homework is checked as students turn it in. Usually, it is returned immediately for them to make corrections on as many problems as possible before we leave for specials at 8:15. Students who have questions also ask for assistance at this time. If a student misses most of the problems, I may choose to work with them one on one during math time instead of having them return to try again on his/her own. This is so that I can gain a better understanding of what is not connecting for them--are they making accuracy mistakes or truly not understanding concepts? When problems are completed correctly, I usually assume that the child has a good grasp on the concept. When helping your child with homework, I only ask that I am aware of any assistance that was necessary so that I can keep that in mind as I plan for your child.

So, how can you really help with homework?
* Use the new stuff I am posting on the blog in the next few days to remind your child of how to solve the problems using the methods we are learning
* Initial beside of any problems that you help your child solve or write a quick note on the paper letting me know that your child did not understand. Some students even jot me a note that they didn't understand how to do something and need my help.
* Let your child know that Ms. Russell has given you permission to work on homework with them and even APPRECIATES it when you check over their work!
* If your child is doing fine with understanding math, but has accuracy issues, remind them that accuracy is a big focus in 4th grade and say something like "Hmmm...I see a few problems on here that are incorrect. I think you know what you are doing but some of your facts are wrong. Can you find your mistakes?" If your child is quick to become frustrated with homework, you may identify the point of inaccuracy (as I often do this in class to show the student in a positive manner, "You were good up until...").
* One practical tip for helping your child understand how to do a problem is to show them how to solve a similar problem using different numbers. After a few practice problems, your child can return to the homework problem and give it a try independently.
* If your child is missing (or misunderstanding) word problems, encourage them to jot down "the mathematical information the problem provides" in a list format. This is the method we use for understanding and solving word problems in the classroom so that language should help them.
* Practice multiplication facts! Multiplication fact mastery (speed and accuracy) is a precursor to successfully mastering nearly everything in 4th grade math--and beyond! You can use a set of flash cards to quiz your child and remove cards that are super-easy for them. Research suggests that students only practice 8-10 minutes in one sitting, otherwise the facts start to jumble in their mind.

Please let me know if you have any general questions about math homework that I have not addressed in this post! Thanks for all you do!

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?

• A typical week in 4th grade math includes 2-3 days of stations with students completing activities at different levels of difficulty. Students may be working independently or 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 time reviewing 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. 

Hopefully, this post has shed light on my approach to math instruction and my strong belief that learning is a process. While your child needs to learn given math concepts, it's not my belief that they must (or even should) master the concept on the day I introduce it. Coming up in our next Math Spotlight, how you can help your child with math homework!

As always, I appreciate everything you do to prepare your child to be ready to learn each day!

Check out the note students received about our Mobile Museum Exhibit Project! We are getting excited! 

Each group will be required to create a mural backdrop, construct a 3-D animal (in art class), design an interactive, hands-on learning tool, and create a group Powerpoint. Within the requirements of this project, students will have lots of opportunity for creativity! We have already set the date for our "Mobile Museum"--March 11th. We hope to see you that morning as we showcase our hard work!