Students Collaborating During Math Instruction

GROUP WORK DURING MATH?

We all know that there are many benefits that come from letting children collaborate and work together on school work. This is usually not seen very often in the mathematics unless the children are playing a game with a partner or at centers in groups. This being said, I plan to allow students to talk with other students and collaborate as much as possible during math instruction. Fostering good academic conversations around math topics will develop their mathematical language, and help deepen the understanding of whatever topic they are discussing.

Ways to incorporate collaboration and conversation within maths instruction

There are multiple ways that I am planning to introduce collaboration within mathematics instruction. One way is to have leveled mathematics groups that meet each week to those children get more individualized one on one time with one another, and me. Another way I plan to include student-student collaboration is within centers. The math centers that I plan to use and create will all engage multiple children at once. This way when the children are playing and working with math concepts they can be conversations about what they are doing. Another simple way to get children talking and using their mathematical language is to ask them ton explain the things they are doing in narrative form. The children can explain a problem to another friend, or even to me in a one on one setting.

impact on motivation

 There is a positive effect on both student achievement and motivation through group work. The discussions that children can engage in during group work can allow students to construct new knowledge and schemas in their brain. The academic discussions amongst peers can heighten students knowledge on a topic and enhance their social skills/content vocabulary. There is also a positive effect on motivation through group work. Children typically get excited to work with friends and peers, so they are going to be more engaged in general, and in turn be more motivated.

Take away for teachers

 It is important to listen to students during group work to get an idea of each child’s understanding. I plan to listen and observe students working in groups in order to identify leaders/followers, and see if the math groups are working effectively within my class. Observing how the groups of children are interacting with each other will help me decide if I need to move anyone within groups, or if certain children are a problem in the same group with other children.

Additional Resources

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5 Math Activities that Promote Collaborative Learning in the Classroom

Collaborative math activities in the elementary classroom can help students move forward along their learning trajectories… and it can be fun! Free PDFs

 

The Role of Technology

Incorporation of Technology

I plan to incorporate technology as much as possible within my future classroom. This can be as simple as using my smart board/projector within lessons, to completely creating virtual lessons/units. With COVID 19, incorporating technology has been at an all time high for teachers, and I’m learning so much within my student teaching that I can take into my future classroom.

Miss. Garrett’s Tech-friendly Planning

 Technology can support almost every part of my future planning. I can use my laptop to research ideas for lessons, to type up the lessons, to create units, to create worksheets and activities, to have a schedule made up for each day,  and to use for incorporation within lessons. Having all of your week’s lessons and materials available electronically will be a huge lifesaver for you, your children, and any sub that may need to jump into your classroom. Without technology there would be a lot less that we can achieve virtually, if school’s were to be closed in the future with COVID 19.

technology use to benefit my students

 Technology can enhance students understanding of math concepts in various ways. Children can access free math apps to use as a practice resource, more practice will grow their understanding of the concepts. Children can also access math games online that would allow them to “play” while learning and practicing concepts. Educational videos are a type of technology that will also benefit the students; embedding videos and simulations within a lesson or presentation is far more engaging than just a powerpoint. Technology will also play a role in higher grades with the use of calculators and digital graphing resources.

additional resources

Teaching Resources & Lesson Plans | TPT

World’s most popular online marketplace for original educational resources with more than four million resources available for use today.

This website linked above is an online database that enhances teaching and student learning. The website is full of resources for teachers such as lesson plans, units, activities, and much more. These sources all come from reliable teachers who take the time to create the content for others to use. The website can be navigated by grade level to ensure what your looking at is appropriate for your students.

Educational Math Games

Have a blast mastering math with our interactive games for kids. Discover adventures in every skill from counting to fractions. Play now!

This website linked above is the perfect resource for free online games for children to use during down time.

SplashLearn: Fun Math & English Program for Preschool to Grade 5

SplashLearn is an award-winning learning program loved by over 40 million kids for engaging math and English practice. Aligned with Common Core and various state standards.

Splash Learn (SplashMath) is one of the best educational math apps to have on your child’s/student’s iPad/computer. It is full of engaging games and activities that promote the understanding of certain math topics.

Measurement in the Elementary Classroom

Teaching measurement in an Elementary Classroom

Measurement is a topic that sometimes gets overlooked in the elementary aged children. Developing an early understanding for measurement is extremely important for young kiddos and can be done very easily. To begin I will focus on using mathematical measurement language with my children. Early measurement concepts typically begin with looking at smaller vs larger objects. These early concepts can be done in conversation alone. Simply asking the children to compare two objects’ size would help them develop this understanding. I would also plan to teach the basic measurement attributes before including the different systems and units for measuring. These attributes include, length, capacity, area, volume, angles, temperature, and time. I plan to incorporate the instruction of these attributes into other subject lessons, and other content areas. One example would be volume and temperature measurement, this can be included into a science lesson where the children do a hands on experiment. Successful measurement instruction must include various hands-on experiences, development of estimation skills, activity-oriented measurement situations, and engaging curriculum.

Measurement Centers

I think one of the most effective and beneficial strategies to teaching measurement is through the use of centers. I have talked about centers before on my blog so my stance on centers is very clear, I love them. I think measurement is the perfect math center topic. The center wouldn’t have to be overly extravagant at all, it could be filled with different objects to measure, and different measurement tools. The center would prompt children to begin measuring with random objects first to get used to the concept, and then it would include rulers and protractors. The center would be the perfect differentiated instruction method for teaching measurement and reaching all of the levels in your classroom.

Enforcing Measurement Concepts at Home

There are many ways that parents can help support their child’s developing mathematical understanding about measurement. First off parents can support their young learners by helping them make connections between comparing and approximation. Parents can casually work these topics into conversation. As a parent, you can ask the child to look at his/her t-shirt compared to your t-shirt. Discuss the t-shirts and use words like bigger, smaller, and longer, or wider. These comparison words will help build your child’s mathematical vocabulary. As your child gets more familiar with this vocabulary you can begin to go more in depth about what those comparison words mean. This can be built up over multiple conversations and times.

            Parents can also support their young learners by asking them to do a task that requires the use of measurement skills. To start off with a simpler form of measurement you can ask the child to measure something with pennies and nickels. The child will have two different measurements which will lead to a conversation on why the penny measurement was bigger. As the parent, you can help explain that because the penny is smaller than the nickel, you need more pennies to measure the length of their shoe or whatever they measured. The other way you can support these measurement skills is by giving your child a ruler and a task. Maybe explain that you need to know how many inches the cabinets are so you can re-do them. Ask the child to measure how wide they are, and how tall they are. This can be done with pretty much any object around the house. At first start out with smaller objects and help the child become familiar with using a ruler and reading it.

additional resources and activities

5 Hands-On Strategies to Teach Measurements for Grades 1-3 | Article

Without even realizing it, we all use measurement in our daily lives all the time. This next article will explore 5 easy and fun techniques for teaching measurement for first graders and older kids.

22 Measurement Activities for Kids at Home or in the Classroom

Measurement activities build kids’ understanding by exploring weight, length, and capacity hands-on! These are great for primary grades.

 

Teaching Geometry In Elementary Classrooms

is geometry only for high-schoolers?

Within my four years studying at Millersville University I personally have not seen many early elementary classrooms incorporating geometry. I also personally do not remember learning geometry until high school. I began to wonder, is geometry only for older children? I have learned through a lot of research that the earlier you introduce geometry, the better it is for your students. The basic concepts of geometry can be included in every classroom, and the earlier you do this as the teacher, the more likely your children will be to succeed in geometry. Geometry and spatial concepts can exceed students numerical skills, as well as provide a context for math concepts.

Geometry Instruction plan

As far as a plan for my future classroom with geometry instruction, I would of course first look to see what my school’s curriculum covers with it. Outside of that information I would plan to introduce geometry within my classroom through the use of children’s literature. One book I have seen that would work well for this is Shape Up! By, David Adler.

This book contains great introductory concepts to geometry, as well as some awesome activities to go along with it. This book could be used in my future classroom as the opener to our first geometry lesson, it would also act as a context to the lesson for that day. I would be sure to develop the children’s geometrical language before moving into advanced concepts. Once this introductory stuff has been addressed, I would move into the big topics for geometry in elementary schools. These include shapes and properties, visualization, transformation, and location. These topics could be taught in a similar fashion, incorporating children’s literature as an introduction and building the concept language. After the introductory information is taught I will use engaging activities, educational videos, and manipulative to help develop the understanding of these concepts.

Additional resources

https://www.the-best-childrens-books.org/Shape-Up.html

This website link above takes you directly to the book I referenced to above, there are many amazing children’s literature books on this website to use within geometry instruction.

https://www.therecoveringtraditionalist.com/geometry-for-elementary-students/

Teaching the Operations

Teaching the operations in my future mathematics classroom will obviously depend on my school district and their curriculum. I do however have some good strategies and methods that I plan to use and incorporate within my school’s curriculum.

Addition & Subtraction

I personally think that addition and subtraction are best taught as a combination of the two. In my future classroom I would plan to begin with addition, the first step would be to introduce and develop the students mathematical language around addition. I will use children’s literature to introduce it, as well as help to develop it. I also will incorporate my Math Word Wall to ensure they can see their vocabulary words, and the meanings. Once my children have a developed understanding of basic addition, I will introduce basic subtraction, beginning with developing their language around it. I can include children’s literature, as well as my Math Word Wall. Introducing subtraction after addition will benefit my students because they can use the methods and skills that they learned with addition with subtraction. Moving up to bigger addition/subtraction problems I would continue this back and forth method of introducing the topic with addition first, developing the skills, then moving to subtraction. Within the teaching of these two operations I plan to use engaging activities, informational videos, manipulative’s, and many other resources.

Multiplication & DivisioN

I personally believe that the same concepts I spoke about above apply with multiplication and division. I think it can be very beneficial to the children and save time for the teacher with class instruction.  I would plan to introduce multiplication first, I can introduce it with children’s literature and educational videos. I would also build the students language around multiplication right off the bat. Once the children learn the skills surrounding multiplication I would immediately introduce the relationship it has to division. If I’m working with the children on a basic multiplication equation, the same numbers would be used to complete the correlating division problem. When you teach them in this alternating pattern and connect their relationship it is much easier for students to understand. I would incorporate engaging activities, manipulative’s, educational videos, children’s literature and much more in doing so.

Additional Resources & Activities for addition, subtraction, multiplication, & Division

 

https://www.teachstarter.com/us/learning-area/mathematics-us/number-operations-us/operations/addition-us/

The website I have linked above is a great resource for addition, subtraction, multiplication, and division activities and lesson ideas. These can be used in a classroom, or with the parents at home.

Grandmabee.com

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The website I have linked above is an amazing resource for explaining how and why you should be teaching multiplication and division together. This article provides great rationale and evidence behind the two subjects being taught together.

Math Centers for Elementary Classrooms

Are they worth it?

Math centers can be very engaging for children during math instruction. They can be used as the perfect ‘brain break’ within your long math instruction time because children will feel like their getting a ‘break’. The best part about this is that while the children feel like their playing they actually are engaging with math in a fun and helpful way. There are many other benefits to incorporating Math Centers as a part of instruction, they can provide differentiated instruction to your class, they can also structure group/partner work within your class, centers can also provide choice to your children.

Future math centers Plan

In order to successfully operate with centers in my future classroom there are many different things that need to happen. First and foremost I need to plan out centers that will spike high-interest, and correlate with my schools curriculum. Once I have created a few math centers I can decide how I plan to organize them in my classroom. In my perfect classroom I would have all of my math centers in organized labeled bins, stored on a shelf. Once I have all of my centers created and stored I would need to use some mini-lessons to introduce the idea and the rules with them. A COVID friendly rule set would include having enough centers that each child could use it. This could also work if one center had enough materials for two children to be playing together (6 feet apart of course). In a perfect world without COVID, all of my centers would allow 3-4 children to play simultaneously.

Addition Facts Center

I have created a couple of my own centers, but my addition math facts center is definitely my best one yet. My addition math facts center is an ongoing center that I am adding different activities too each week based on the curriculum. Once the addition portion of our curriculum is over the center will be complete with activities that range from the most simple addition facts, to the most complex we do in second grade. Each activity that I create for the center is differentiated to reach three learning levels. Each activity has a green (below level), black (on level), and red (above level) set so that all of my students will be able to use it in a way that caters to their individual learning level. I will be able to use this math center in my future classroom one day. I also now have a good example of a ‘basic math fact’ center so that I can create more for different operations.

Additional Resources for creating and Planning math centers

 

The Ultimate Guide to Math Centers – Mr Elementary Math

The Ultimate Guide to Math Centers – Find everything you need to know about math centers, from plannning to organizing to management.

NAIS SSO

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The Use of Children’s Literature in Teaching Math

Why include it?

Children’s Literature can be incorporated into the school day regardless of the subject. Some teachers that I have observed over the years seem to keep reading separated to ELA time. Children’s literature has many proven benefits in aiding to teach other subjects including mathematics. Some of the many benefits are, children’s literature provides a context for problem solving activities, it can advance mathematical thinking, it creates an integrated lesson with more than one subject area, and it can promote the use of manipulative’s described within a story.

Children’s Literature used to support Varying needs

I plan to  incorporate children’s literature into  my mathematics instruction to benefit all of my students. The incorporation of children’s literature can also be used to support the varying needs of my future classroom. I know math can be difficult for some children, and incorporating another subject area gives that student another opportunity to be interested in their lesson or topic at hand. The child who struggles in math may love reading and they would be so excited to see a book about your math topic of the day. Using children’s literature can also be used as an extension for a gifted students if they are left bored during an activity, these students can spend time reading a book about their topic to grow their understanding.

Current Research Behind it

While looking for some current research to back up this strategy I came across an incredible article, Using Children’s Literature to Teach Mathematics: An Effective Vehicle in a STEM World, by Joseph Furner. The article focuses on the many benefits of incorporating children’s literature, and how it can help engage children’s imaginations with mathematics. The article also addresses many real life examples and books that you can use in your elementary math classroom. The article is linked below if your interested in reading all of the great information within it.

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Additional Resources

Motivational Math Lessons Using Children’s Literature

Motivate your child to learn math using literature. Use these tips to enhance their learning abilities and expose them to various learning methods

 

All About Manipulatives

Developing Math Concepts through the use of manipulative’s

Developing math concepts through the use of manipulative’s is a strategy where teachers use tangible materials to aid in the learning of young students. The use of math manipulative’s have been proven to strengthen the development and understanding of math concepts. I have linked below an article that shows a study that was performed in a Second Grade Classroom dealing with manipulative’s. The article was published in 2017 so all of the data is very recent and relevant. The purpose of this study was to test the impact of manipulative use on Math Test scores for a group of second graders.  The study proves that there’s a clear relationship with the use of manipulative’s, and improved test scores. Feel free to read the article to get more information below:

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Covid Friendly Manipulative’s

Prior to COVID 19 math manipulative’s could be used in small groups and shared amongst students. Now that there are social distancing rules within schools and sharing limitations, manipulative’s need to be stored and used in different ways than we are used too. Math manipulative’s can be stored and cataloged in many different ways, but I think the best way is to have a math bin for each student and that’s what I plan to do in my future classroom. My future classroom would have a math bin for each child that is numbered, and each math bin would be full of various different manipulative’s. These bins are COVID friendly, the children wouldn’t share or touch anyone else’s bin/materials. These could also be sent home if learning becomes virtual at any point in my future teaching years. I would plan to store these math bins on a shelving unit that all of the children could reach. This way all of the math bins/manipulative are in one place for the children to access.

How to use them?

I plan to incorporate the use of math manipulative’s as much as possible with the children. They can be incorporated with early number sense by using counters to help a child count and understand cardinality. Manipulative’s can be incorporated with mainly all of the operations, allowing children to physically solve a problem and see the quantities. Base ten charts and blocks can be used when learning place value, and it’s meaning. Plastic shapes can be used within geometry lessons, and to help develop spatial awareness. These are just a couple of the many ways I plan to incorporate the use of manipulative’s in my future math class.

Resources for math manipulative’s

Math Apps

Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

The website I have linked above takes you to an entire list of free virtual math manipulative apps. These are especially useful right now with virtual teaching and learning, and I think they are an amazing resource to view.

Developing the Language of Mathematics

Time crunch

When working with young children there is always pressure on the teacher to follow a set curriculum, and stay on track with the weekly schedules. More frequently than not I have witnessed a lot of elementary mathematics classroom’s that don’t really do the early number sense and language of mathematics justice. I believe that this may be a trend because some teachers don’t think they have time for it. Who needs a vocabulary lesson in mathematics? It’s all about the numbers right? Wrong!  Ensuring that there is a strong development with early number sense, and the language of mathematics is crucial  for being an overall successful math student.

The language development process

The development of a child’s mathematical language will progress in stages,  this can’t just happen overnight. Typically a child will begin by using their own student language for describing math concepts,  this will progress into a  materials based language, and finally into a mathematical language. All of the strategies you chose to do as the teacher will help the students progress from one to the next.

Where to start? vocabulary

 There is a direct relationship between vocabulary development and students’ ability to communicate mathematical thinking. If a students math vocabulary development grows, their ability to communicate their mathematical thinking will also grow. Vocabulary is essential in being able to comprehend and speak in the English language, this should not be any different for a students mathematical language. There are many different ways to develop a child’s math vocabulary and I plan to focus a lot on this with my future classroom.

Vocabulary Substitution

One of the strategies I plan to use is, Vocabulary Substitution. This is a simple strategy for the teachers to perform in order to develop and strengthen their students vocabulary. This strategy doesn’t have a specific instruction list or set of rules, it’s simply a way for teachers to talk to their students and foster academic conversation. For example, if you hear a student trying to explain a math concept and they aren’t using the actual mathematical language just substitute the correct vocabulary word for what they are saying. If you hear a student say, “I’m putting these two numbers together to make a really big number”, you could respond to them “Yes, you are adding those two numbers!”. This may seem so simple and it’s probably something you do without even realizing your using a strategy; but the more the children hear and converse using the correct math language, the more developed it will become.

Math word Wall
http://democlassroomsharing.blogspot.com/2011/03/math-word-wall.html

One other simple way to include mathematical language and vocabulary into your classroom, that I plan to incorporate is the use of a Math Word Wall. As we talk about and come across new math concepts I will keep track of the words we are using on a Math Word Wall. Just like teachers use a sight word wall for ELA, I think this concept is just as useful for math instruction. Every time we define a math vocabulary term within a lesson, I would stop and add it to the Word Wall. In my perfect future classroom this word wall would have each math term, some synonyms for it that the children may be more familiar with, and a kid friendly definition for them to view.

Resources to support this & give more information

Math Word Wall

This is the math word wall Marie created for her Grade 3 students. There are many purposes of a word wall: – get students to spell a word…

This first link takes you to the blog where I found the great image of a math word wall. There is a lot of good information and ideas on Marie’s blog.

Math Resources For Teachers | ORIGO Education

Our resources include our blog, webinars, events, free resources, news, and much more! Browse and download our library of math resources for teachers.

Miss Garrett’s Mathematical Mindset

Current Mindset Trends

Having the correct mindset is important in daily life for everyone. This is something I find extremely important for children in math class. Over the course of my time at Millersville, I have had four different placements where I’ve gotten the opportunity to observe and work with a variety of children. The overall theme that I’ve noticed with math class is that some children have a closed mindset towards math. Children usually think that they are either a math person, or not a math person. This mindset creates a false identity that the children carry with themselves all throughout grade school. We need to change this so that each child knows they have the ability to do anything they set their mind too.

Miss Garrett’s Mindset

It is going to be one of my personal goals to ensure that children look at mathematics with a growth mindset. A growth mindset in mathematics is the belief that intelligence can be developed for the subject. You aren’t just born without maths intelligence, but you need to work towards building this intelligence. Building this intelligence and mindset requires making mistakes, learning from those mistakes, and coming back stronger because of it.

Mistake Making

One of the biggest areas that I will focus on in my classroom in order to achieve a growth mindset in mathematics is making mistakes. This might confuse you at first, but let me explain… It is incredibly important that we change the attitude towards making a mistake and automatically being wrong. Making a mistake has been scientifically proven to grow your brain. When you make that mistake, and struggle with a concept or problem, our brain our growing from it. Children need to understand that making a mistake is an opportunity to grow and become stronger. One way I plan to make this clear in my classroom is by ensuring that the classroom environment is a safe and welcoming place. The students need to feel a sense of trust within their teacher and their peers. If this environment can be achieved the children will be more comfortable being vulnerable and wrong in front of one another. During a lesson or example if I make a mistake I will point it out to the children and show them that I, along with everyone else, am not perfect. Pointing out my mistakes and being okay with it will set a good example for the students I am teaching.

Resources to support this

Below are two amazing resources to gain more information about this topic, and resources for supporting a growth mindset in your math classroom.

Healthy Habits for a Growth Mindset in Math

Here’s a helpful list of healthy habits to enable a growth mindset in math, plus a free downloadable poster for your classroom.

A Growth Mindset in Math – blog – Mike Anderson

Why are timed tests, ability grouping, and memorization all math practices to give up? Jo Boaler explains how to help kids develop a growth mindset in math.