Final Reflection!

WOW, this is my last math blog post for the semester and boy did that fly by. I remember starting off the semester feeling completely uncomfortable and stressed out. Math was never my favourite subject when I was growing up. I tolerated it because it was mandatory but I never truly looked forward to it, instead I dreaded it. I thought math just wasn't my thing, that I was simply not a math person. However, this course and Pat have both made me realize that everyone can truly be a math person. This course expanded my horizons and I saw math in a whole new light. Math can be fun, interactive and have multiple solutions. Math can incorporate literature, technology and manipulatives. Math is taught today in a way that I never had the privilege of learning. Now being a teacher candidate and a future teacher of math for my grade 7s and grade 8s, in January and February I could not be more thrilled to teach them the way Pat has taught me. The math class this semester has truly prepared me and provided me with the knowledge and vast amount of resources to teach my future students. My confidence has been boosted when it comes to math and I can only hope one day to be as skilled and charismatic as Pat was in front of our math class.

Some key things I took away from this course included the use of manipulatives, providing students with open questions, creating a growth mindset, encouraging mistakes, and allowing students to explore math in a way that makes sense to them!

MANIPULATIVES 

Manipulatives are huge for students of all ages and all math levels. Whether a student needs them or not, all students should be encouraged to use the manipulatives that they are provided. I am an extremely visual learner so I find that manipulatives; whether it is number blocks,  geometric shapes or fraction strips they all help me to visualize and understand math in a creative and easy way. Some students might find that if they use manipulatives they feel that they are "stupid", this is not the case, and it should be addressed at the start of the math year. Manipulatives help students to check their work as well as understand and communicate what they are learning in math. Furthermore, the use of children's literature is huge! Everyone loves being read to, even our teachers college math class does! Thus, I feel starting off a math lesson with a story can help promote students critical thinking as well as their creativity. Students can relate the story to their lesson and develop a better understanding for what they are learning in math. Reading in math is crucial for understanding what the question is asking the students. As well, reading can help students to understand how subjects can cross over and tie into other subjects. I know even in my grade 7 and 8 classes I will try to read to my students and show them the importance of literacy in math.

OPEN QUESTIONS 

Additionally, another key idea that I picked up on in my math class was the importance of providing students with open questions! Students need to think outside the box and attempt to solve for a question in a way that makes sense to them. If we provide our students with open questions they can constantly solve and improve upon what they are looking for. Open questions promote critical thinking, creativity and allow all students to get started. Open questions can go on forever and have multiple right answers.... something I was never introduced to in math. When I was taught math there was one right answer and one way to solve for that answer. We never had a choice, and this is huge for our students. Our students need freedom to learn in a way that suits them, open questions allow this to happen. 

GROWTH MINDSET

Having a GROWTH MINDSET is imperative when it comes to teaching and math. We need to provide effective feedback to our students and encourage them to constantly think outside the box. The idea behind a growth mindset is that our skills and intelligence are constantly growing and evolving. We need to keep trying and have a positive attitude in everything we do. Students should be encouraged to learn from their mistakes and keep on learning. I  have seen the emphasis and importance within all of my classes at Brock as well as at my placement. Every classroom highlights the importance and benefits of a growth mindset and how it should be a part of every students learning.

MISTAKES 

As Miss Frizzle from the Magic School Bus cartoon once said, its time to take chances, make mistakes, and get messy!!! I love this idea. It is extremely crucial that we encourage our students to try their best but to also not be afraid of making mistakes. Some of the most successful people in the world failed before they became who they are. We LEARN from our mistakes and can grow as a group and individually. Students need to stop stressing about their marks and thinking that they look stupid if they don't get a question or ask for help. There is no such thing as stupid question and our students need to understand this concept. All we can do is improve from our mistakes. They are excellent ways to move forward in life and to LEARN!

EXPLORE

EXPLORE!!! Students need to be encouraged to go outside of their comfort zones and take on new challenges everyday. Students need to explore math in fun and interactive ways like never before. As they are exploring math they will learn more about themselves as well as the world around them. Encouraging students to explore and think for themselves is vital to their progression and successes in life.

In conclusion, this entire experience has been one hell of a ride. I have learned things about math that I didn't know before, I have refreshed my mind on topics I once loved and I have developed new feelings towards math that I thought would never be possible. This past semester has been extremely enjoyable as well as eye opening and rewarding. I have learned much in the past twelve weeks and I intend on taking everything that my fellow classmates and Pat have taught me, out into my first teaching block. Thanks for an excellent first semester of teachers college! I cannot believe its already over, the time has flown bye. 

Until next time, 

Cheers, Courtney Helt 

Have a very Merry Christmas to all of my fellow teacher candidates and viewers of my blog!

Data Management & Probability- Week 10

Different Types of Graphs, Tables, Charts. Google. 2016

This past week was all about DATA and PROBABILITY! We started off the class with Pat asking a question which created an open discussion about estimating! We were asked, "Did anyone do any estimating today?" Everyone looked around for a moment and then you could see the light bulbs go on in everyone's minds. OF COURSE WE DID! Our days are filled with estimating, my peers began sharing their estimating experiences. For example, some estimated how long it would take to get to school? How much farther can I drive my car before getting gas? Can I get my forum posts done before math class? If it's raining will there be more traffic getting to school? The estimates went on and on, all different for each student but also many students had experienced the same type of estimates.

This activity was a great way to open up the lesson and have students apply a math topic to their everyday lives. As future teachers we will get the same old question, "But Ms. Why do we have to learn this, I'll never use it in my everyday life?" or, "Ms. How does this apply to the real world, math is so stupid." I have learned throughout this course that it is important to provide learning opportunities that coincide with everyday experiences, in order for students to be successful in math. If students can understand math concepts and see that they apply in everything they do, the students will take more away from the lesson and also look at math in a fun and informative way.

Pat also showed us an excellent video about Growth Mindset. Below is a cute video that students of all ages can relate to. The video can also relate to other subjects not just specifically math, and encourage students to have a Growth Mindset.



This video is part of an adorable collection of videos that talk about Growth Mindset. There are also videos teaching students about empathy, perseverance and many more.

Pat also showed us all the different ways in which we can teach our students to display data. She brought in a cookie jar filled with oreos and had everyone in the classroom guess how many oreos were in the jar. Once everyone guessed we put our information onto a stem and leaf plot to see what data the class had gathered. This is an excellent way for students to use manipulative's. Both the cookie jar and chart paper can help students see and therefore understand math concepts better. It is important to provide a fun and interactive learning environment.

As well, Pat showed us various ways to graph information using different graphs, charts, tables, scatter plots, and histograms through online resources as well as good old fashioned chart paper. All of these tools and methods can be used to display different topics related to probability. It is important to provide our students with online resources that they can use on their computers at home, as well as interactive resources such as the smart board. These tools help to make learning fun for students of any age. As future teachers it is key to provide our students with lessons and resources that they can relate to and find appealing.

Additionally, we used linking blocks, an EXCELLENT MANIPULATIVE! (Manipulative's are my favourite, and the key to success in any math classroom), to also show different ways in which data can be represented.

Below are two pictures that I took in class.

This first picture is of the problem that was presented to the class. The idea behind the question is to create bars for each original number presented in the problem and then figure out how to make each bar the same length, therefore levelled.


The second picture is of the block towers I created. This picture shows how I levelled the bars using the connecting blocks to solve for the problem.

In conclusion, the reason Data Management is so important in our world is because it helps everyone to make predictions as well as estimates. This helps individuals to know what to expect, who doesn't want to be prepared. This week provided me with some valuable insight. For my first teaching block I will be teaching the unit on Data Management and Probability. This week, Pat provided her class with so many valuable resources and insight into how to properly teach this unit. I definitely feel more prepared as a result of Pat's lesson and the important information that our course textbook highlights. There are tones of fun and interesting activities that I can pull from our course text to help me teach my first math unit to my grade 7s and 8s. Hopefully it will be a great success!

Wish me luck!

Cheers, Courtney

Formative Assessment- Week 9

This week was all about Formative Assessment! In our textbook, Making Math Meaningful to Canadian Students, K-8 Assessment is defined as, "the gathering of data about student knowledge and or skills, either informally or formally". (page 36) As well, there are three different versions of assessment that we have been learning about in all of our classes, these include: Assessment for Learning, Assessment as Learning, and Assessment of Learning.

Below are two cute and informative videos about formative and summative assessment.



Assessment for Learning, is formative not summative. It can be defined as, "designed primarily to help the teacher tailor instruction to the needs of the needs of the student." (page 36)  This type of assessment is designed to give teachers information so that they can modify and differentiate teaching and learning activities. Teachers must provide feedback so students can advance their learning. Assessment for learning is done all the time through LISTENING!

Assessment as Learning, is a form of assessment for learning. It can be defined as, "focuses on the importance of students thinking about their own performance and learning from it." (page 36) This type of assessment involves metacognition for students. The assessment is the learning and allowing students to improve their learning when the teacher provides examples.

Assessment of Learning, has more than one purpose. It can be defined as, "designed to inform a variety of stakeholders about what a student's knowledge and skills are at a particular point in time." (page 36) Assessment of learning provides the basis of what is reported to parents and school officials. This type of assessment does not have to be only at the end of the course. Assessment of learning is used to confirm what students know and if they have achieved the curriculum expectations.

Chapter three of our math textbook is filled with information about assessment and evaluation, different ways in which we can assess and evaluate our students, different tools to use, strategies, plans and examples for how a teacher should assess students in regards to math. Pat taught us some key ideas about assessment this week that are vital for any teacher.

As we walked into math class this week Pat let each student pick a popsicle stick. We were asked to get into groups of six with students who had popsicle sticks numbered 1-6. Therefore, this activity allowed us to have some choice to pick our groups but not total control over our groups because we had to find students who had popsicle sticks numbered 1-6. I like this idea for creating groups because it allows students to go outside their normal comfort zones/groups that they always choose.

The objective of this activity was to move around with your group of 6 from station to station and complete the activities. At each table groups were tasked with completing the different math activities by using the clues provided. Each student had their own clue and therefore everyone was needed and had a part to play in order to work together and solve the problem. Thus, no matter how students feel about participation and math every student has to provide their clue. We were allowed to share the clue verbally but could not give it to our group members.

Furthermore, each activity center had different manipulatives that our groups had to use to solve the problem. For example, one center had toothpicks, one had a hundred chart, and one had linking cubes. Below are pictures that I took from the different activity centers.

Courtney Helt, 2016

Courtney Helt, 2016

Courtney Helt, 2016

As well, in class we did a clapping activity to show the importance of discussing learning goals, success criteria and climate. Students need to know what is expected of them. For example, the first person clapped and there was no criteria as to how the student should clap or what expectations the teacher had. As each person clapped they received more feedback and criteria and therefore they did better. Thus, it is important that we involve our students in their own formative assessment. It is proven that there will be greater positive results when students take part in their own goal setting.

ASK QUESTIONS STUDENTS CAN ANSWER!!

The Fundamental Purpose of Assessment & Evaluation in math class is to IMPROVE STUDENT LEARNING!

The Keys to Student Success for Assessments:
1. Give students feedback all the time!
2. Monitor progress- gather evidence in a variety of forms to illustrate student's learning & growth
3. Teach in a cyclical way
4. Encourage students to take responsibility for their learning
5. Keep assessment simple = small # of learning goals

As well, we discussed the importance that Descriptive Feedback has for students. Below is a picture of  what is Descriptive Feedback and how it can help students to improve and move a student one step further. There are three things to keep in mind when it comes to providing effective descriptive feedback. 1. List the strengths/assets of the solution. 2. Wonderings- I wonder why you did this? I wonder if you can go further? 3. Challenges/ Fragile Concepts - Next steps- SPECIFICALLY what they need to focus on.

Courtney Helt, 2016

In conclusion, the main idea I took away from this week is that students can be assessed in a variety of ways, for a variety of activities, constantly. The reason for Assessment is to IMPROVE STUDENT LEARNING! To make Assessment successful for students, BE CLEAR ABOUT THE PURPOSE OF EACH ASSESSMENT ACTIVITY!

Cheers, Courtney!

Measurement -Week 8

Teaching Elementary Mathematics, TeacherVision.com. Picture. [Online Image] Google.

This past week was all about Measurement! In our textbook, Making Math Meaningful, measurement is defined as, "the process of assigning a qualitative or quantitative description of size to an object based on a particular attribute."(page 411) Specifically this week we looked at measuring area and perimeter of certain shapes. Our opening activity was an excellent game called, "I have... who has..." This game can be used for multiple subjects to test kids on what they already know in a fun and intriguing way. The premise of the game is this, students each have a card. It is titled "I have" and the state the clue on it and say, "who has?" Then the next person in the class who has the answer to that card states what they have and their clue. For example, "I have, an equilateral triangle. Who has, a shape with six closed equal sides in length?" Someone would answer, "I have a hexagon, who has..." and the game goes on until everyone in the class has stated their clue and the answer and it all goes back to the beginning.

This game is terrific because it allows students to think on their feet and they have to use critical thinking skills for understanding what the question is asking them and to be aware of what questions are being asked in order to answer appropriately. As well, students can work with their table mates to try and figure out the answer to their questions. This game helps students to overcome their math-phobia as well as creates a challenge in which students will be successful. This game went very smoothly with our class and everyone thoroughly enjoyed it. I could see myself using this game in my grade 8 class to review with students certain concepts that they carried over from grade 7 or to quiz the class on certain terms.

Following this opening activity Pat started off a problem to introduce area and perimeter to the class. She presented a  very open ended question that relates to herself as well as her students. The question had a problem involving rabbits, cages and Pat's precious vegetables. Every year in the Fall, Pat changes up her garden. She gathers all the fencing that was used to keep the rabbits out of the cages and creates a plan for next years garden. She asks her family for help, mainly her competitive brothers to try and create 2 rectangular cages that use the same amount of fencing but one cage is 6 square metres greater than the other. What could the side lengths be if the sides are whole number values?

As we were solving this problem with our partners Pat reminded us to keep track of what we were solving in order to understand how far we've gone. This is an excellent way for students to see the work they did by showing it. This helps the students to understand either where they went right or where they went wrong. Pat provided us with manipulative blocks as well as whiteboard graph paper.



Courtney Helt 2016

Above you can see the two different ways in which I solved and drew out the gardens. We knew that the perimeter for both gardens had to be even in order to create a rectangle that was 6 units larger. The perimeter for both gardens is equal to 22, but they both have different areas, 24 metres squared and 30 metres squared. We came to this answer after trial and error of drawing different shaped gardens and going through various multiplications.

Garden 1: Perimeter= 22m
-8m x 3m = 24m squared

Garden 2: Perimeter=22m
-6m x 5m = 30m squared

In Making Math Meaningful, there are three stages that teachers go over with students and they apply to both perimeter and area. The stages include:

-Definition/Comparison: "Students begin to learn to define the measurement, and become aware of and apply a process for comparing items."
-Nonstandard Units: "Students continue to define the measurement while they learn to measure with nonstandard units."
-Standard Units: "Students learn to use measurement tools to measure with standard units."
(page 414)

Area and Perimeter Lesson. Picture. [Online Poster] Google.

Lastly, Pat discussed with the class what was involved for a Guided Inquiry Lesson:
-Inquiry Based
-Develop challenging concepts
-Set-up so small groups can proceed independently
-Still need teacher to facilitate
For example, the lesson would take place after a grade 8 class did an inquiry to discover the relationship between diameter and circumference, and between radius and area.

In conclusion, this week I learned that trying new activities that break me out of my math-phobia shell are extremely helpful and rewarding. It is important to remember to take chances and make mistakes. It is also important to remind our students that making mistakes is imperative because they help us grow and change. We learn the best when we are making  mistakes!

Till next week!
Cheers, Courtney!



Geometry & Spatial Sense - Week 7

Geometry Wordle, Picture. [Online Image] Google.

This week was all about the shapes! Geometry and Spatial Sense was probably my favourite unit back in elementary school. I myself am a very visual and concrete learner. Therefore, getting to see what I'm doing through the use of manipulative's and examples in my own hands, is the best style of learning for me. I also believe students, especially in the elementary grades learn math the best and actually comprehend it when using manipulative's.

                      Geometry Refrence, Picture. [Online Image] Google.                 Geometry 2015-2016, Picture. [Online Image] Google.


We started off the lesson by identifying Key Terms. These included:
-Similar: In math it means the same shape but could be different sizes, colours etc. Shapes are similar when, "they have the same shape, with sides in proportion to one another." (Making Math Meaningful, page 371)

Quiz & Worksheet- Similar Shapes in Math. Picture. [Online Worksheet] Google.

-Congruent: In math means equal, colour does not affect this. Shapes are congruent when, "one can be transformed into the other through a series of flips, slides, and or turns." (Making Math Meaningful, page 370) Sides and angles of a shape can also be considered congruent.

BBC: Congruent Shapes. Picture. [Online Image] Google.

****Everything congruent is similar but everything similar is not congruent!****

Pat taught us that engaging the students in an activity that they can relate to will not only create a fun learning environment but the student will also take more away from the lesson and remember what they are learning. This has been a key idea that Pat has been trying to reinforce throughout ALL our math classes!

Another fun activity we did to kick start our symmetry lesson was getting the entire class to stand up, look at each other and try to identify who is symmetrical, and who is not? I could see this working in  a junior to intermediate classroom exceptionally because again, we are involving the students and associating them to their learning by using real-life concepts to relate math.

Face Symmetry of Celebrities. Picture. [Online Image] Google.

Following this we brought reading into our math lesson.... READING! I know, who would have thought that reading a story goes along with math class. Our math textbook, Making Math Meaningful, provides a list of books at the end of each chapter in which teachers can use as resources to help teach their students math in both a fun and informative way. I believe students love to be read to at any age, so by providing a scenario in which the class can be read to but also taught key math ideas is revolutionary. I would have LOVED this when I was in elementary school.

The book we read was called The Greedy Triangle. The book was about a Triangle who was dissatisfied with how many sides he had. Therefore, he went to the shapeshifter to constantly add more and more sides thinking this would make him happy. The poor triangle had so many sides that he ended up loosing his balance and got in a bad accident. As a result of this, the triangle finally realized that he was happy being himself. This book mixed math and children's literature along with moral values into an excellent combination for learning.



The Greedy Triangle. Picture. [Online Image] Google.

Furthermore, this week was the week I did my lesson plan presentation. I chose the topic of symmetry, specifically reflective symmetry of 2-D and 3-D shapes. The line of symmetry is, "when one half of a shape reflects onto the other half across a line." (Making Math Meaningful, page 354) Many shapes can have one or more lines of symmetry because the more sides there are on a regular polygon, the more lines of symmetry there are because the shape is resembling more and more like a circle. (page 354)

Reflective Symmetry: Is also known as reflectional, or mirror symmetry.
In Making Math Meaningful, reflective symmetry is "when one half of the shape is a reflection of the other half." (page 354) Both 2-D and 3-D Shapes can have reflective symmetry.
-2-D Shape: the reflection is across a line.
-3-D Shape: the reflection is across a plane.
-AND BOTH have opposite sides that are mirror images.

BBC Reflection Symmetry. Picture [Online Image] Google

The lesson and activity was designed for a Grade 4 classroom and I conducted it to my associate teacher candidates. I produced a mini lesson about Symmetry to the class, and then read the scenario and task out to my peers. The task was to follow the treasure hunt map by identifying which shapes are: symmetrical, asymmetrical and how many lines of symmetry does each object have. Once completed, the students found the treasure, "leftover Halloween candy". I feel like this activity ran smoothly and that the class enjoyed it.

Before I did my presentation I felt nervous but I did not realize how nervous I actually was until I got up there. I realized I needed to slow my pace when discussing the activity to the class. I talk REALLY fast when I get nervous so it's good to remember to SLOW DOWN! Especially when teaching in the elementary grades, in order to make sure students understand the concepts that you are teaching.

Courtney Helt



Courtney Helt

Geometry is a topic that students can get excited about! If you want to be an inspiring teacher get the students up and moving, provide worksheets and different manipulative's that the students can engage with. Use multi-media, your smart board so students can physically move shapes and identify their properties. There are thousands of fun and interesting ways that a teacher can teach Geometry. Whether you explore Pinterest or online resources, teachers just have to be willing to go outside of their comfort zone and explore the wonderful possibilities in which you can teach math! This will create a fun and inviting learning environment, in which your students will be successful.

 

KEY TAKE HOME MESSAGE: GEOMETRY YOU GOTTA DO IT TO BE SUCCESSFUL!!!!

 

 

Cheers, Courtney!

Patterns and Algebra - Week 6

Morrison, Chantelle. 2015- Term - 1 Maths - Patterns and Algebra. Picture, [Online Image]

Week 6 was all about Patterns and Algebra. Our course textbook states that, "Patterns represent identified regularities." (Making Math Meaningful, page 606) Thus, patterns always have an element of repetition, whether this is the same repetition repeated over and over again or a "transformation," such as adding 1 or subtracting 1. The textbook defines Algebra as, "a way to represent and explain mathematical relationships and to describe and analyze change." (Making Math Meaningful, page 606)


Helt, Courtney 2016.

Our opening activity this week caused my group a massive headache in the beginning. Consequently, as we received greater clarification from Pat we found ourselves on the right track. This activity proved that it is essential for providing students extra detail when explaining a task in order to set them on the right course. I think every group struggled with this activity in the beginning but as we received the scaffolding from Pat, we were victorious!

The activity asked groups to sort the 16 cards into four groups by matching up the model, table, graph an equation. Easy right? Wrong! There were four blank cards that we had to use to complete each expression and this caused us to mess up.

However, learning from our mistakes is a key part of the education system and a part of life. If we never make a mistake we will never learn.

Moreover, in this lesson we learned more about pattern rules. Students were asked to model the equation by using different coloured cube links. These manipulative's provide excellent feedback and understanding for the student as well as the teacher.

Below is a picture of a pattern we were discussing in class. Here we can see that the pattern starts off with 2 red blocks and 1 green. As you go along the pattern 1 green block is added each time. We had to create an equation from this. Our equation was b= total # of blocks, in which we were adding 2 each time and n= the pattern going up by 1 green each time. Thus, b= 1n +2. We guessed the rule by creating a  T- Chart, in which guess was n and t was total. So, starting at 1, the total number = 3, starting at 2 the total number = 6. Therefore our total = 3n. The patterns can be changed, manipulated and made more difficult for students in the higher grades.


Helt, Courtney 2016.

Below is a link to the Three- Part lesson in Mathematics. We had to view this link before last weeks class. It is a great tool that can help students understand how to effectively create a concise 3 part lesson plan.
http://www.curriculum.org/secretariat/coplanning/learning.shtml

As well, here is another great video by Khan Academy that helps to explain math patterns. Khan Academy is a superb tool that all teachers and students should be familiar with.




In conclusion, the key message I took away from this week was the idea to never give up! No matter how hard the work is we should always be encouraged to strive to do more and to be better. As well, both students and teachers should never be scared to make mistakes and get something wrong. No one is perfect! Everyone makes mistakes! Furthermore, it is how we act accordingly to those mistakes, this is what makes us who we are. As a great cartoon and inspirational teacher would say, "It's time to take chances, make mistakes and get messy." - (Mrs. Frizzle, Magic Schoolbus)

Till next week,
Cheers Courtney

Integers and Exponents -Week 5




iPracticeMath. Integers. Picture [Online Image]

This week in math class it was all about Integers! Now, when I first heard the word integer I somewhat feared it. However, to my surprise integers are nothing to fear but something that we are surrounded by everyday. For example, driving uses integers, positive and negative experiences could be classified as integers, the stock market, time lines in history (AD and BC), above and below sea level, gambling and temperatures use integers. Below is a great video from last weeks Building Background Activities, it is about the use of the integers in the real world in regards to temperature changes and maintaining the proper temperature for an ice rink. This video helps to put into context the importance that math plays in our everyday lives. If students can understand that math is all around them and used everyday this will eliminate the "why do I have to learn this" type of questions.

http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/video_interactives/integers/integersSmall.html

Definition of An Integer:

An integer IS a whole number that can be + positive, - negative or 0 zero. An integer is NOT a fractional number or a decimal. Thus: Integers ARE: 0, 1, 2, 6, 13, 120 etc. Integers ARE NOT: 1/4, .05, 25/50, 0.07, 8.9 etc.


Online Math Help and Learning Resources. Properties of Integers.
Retrieved from https://www.google.ca/search?q=integers&biw=1607&bih=792&source=lnms&tbm=isch&sa=X&sqi=2&ved=0ahUKEwjy37W22IbQAh
XMxYMKHYEOAC0Q_AUIBigB&dpr=0.85#imgrc=lBMaPOfePd9VLM%3A

Spencer, Erica. Picture [Photograph]
Retrieved From
https://www.pinterest.com/pin/297026537907027162/

In class we learned that the biggest problem involving integers is the fact that teachers who teach rules that don't apply to integers and make students memorize them. For example, a common rule that many teachers teach their students is that, "two negatives don't make a positive for adding, however, it does for multiplication." Thus, students need to forget the rules their teachers have taught them in regards to integers and learn the proper way to understand them.

Math Congress:

As well, in this past math class we learned about the idea of a Math Congress. We conducted it ourselves in regards to a problem our teacher assigned. A Math Congress can also be referred to as a gallery walk. Students work in groups to solve a problem and then write about their problem on chart paper. The students product's can be either hung up or left on the desks because each group will go and visit the various charts that other students have created. A math congress promotes creativity,sharing and thinking among students in various grade levels. It involves hard work by each group because the following work will be assessed by their peers. This is an excellent tool because it allows students to see how their peers are learning and what similarities and differences that they may come across.

 

CLIPS:

Furthermore, we learned about another key resource, CLIPS- Critical Learning Instructional Path  Supports. This is a multi-media resource in which the learning objects are focused on the key topics and identities as needed by a significant percent of students. CLIPS provides teachers with gap closing material for teachers which was originally meant for students to catch up. Students can get into small groups or work solo while other students move along. CLIPS, allows teachers to go through different lessons which tell you what you did right and wrong. Teachers pick the grade level they want to focus on, there are built in manipulative's and clues that can be clicked on for extra help.

 

Conclusion:

As a class we are still adding to our list of ideas for, What Makes a Good Problem,below is the collective list that we compiled together last class. It is important to keep these aspects in mind for when we are creating math problems and encouraging students to create their own problems.

1. Wide Base = everyone can start
2. High Ceiling = potential to create discipline
3. Soft Language
4. Relevant = to the class, lesson and students
5. Multiple Ways To Find The Solution
6. Use Different Manipulative's
7. Work Together = support & help
8. Creates Discussion
9. Challenging

Till next time,
Cheers, Courtney

Fractions Continued Divide and Conquer -Week 4

Last week's math class was a continuation from Week 3. In week 3 we learned the proper way to add and subtract fractions using various manipulative's. This past week we continued the fabulous journey of fractions and learned the appropriate way to divide them. Back in elementary and high school I was taught to invert the fractions and multiply, this was the only way we were taught. Now, being a young student who didn't like math to begin with or really understand it, this was extremely confusing to me. Fast forward to several years later to my teacher's college J/I math class. I have now learned that this is totally the WRONG way to teach kids how to divide fractions. Not only is this way wrong but it is also extremely complicated. PSA: dividing fractions does not have to be complicated, I'll show you below.

When dividing fractions we can remember that dividing is the same as multiplying. We must remember to just divide across the fractions as we would multiply across the fractions. We do not need the reciprocal anymore, there is no need to invert the second fraction and multiple!

MathChat. How to Divide Fractions From Annoying to Fun! (November 19 2008). Math, [Online Image]. Retrieved From https://mathchat.me/2008/11/19/dividing-fractions-from-annoying-to-fun/

For example: 6/12 divided by 2/3
Solution: divide the numerators by each other: 6 divided by 2 and divide the denominators by each other: 12 divided by 3.
Answer: 3/4

Division Problem Example: Kate divided a fraction less than one by another fraction less than one and came to an answer of 3/4. What might her fractions have been?
9/16 divided by 3/4 = 3/4
Thus, you simply divided the numerators by one another and the denominators by one another.

HOW SIMPLE WAS THAT!

Furthermore, another key aspect that I was taught in elementary and high school was that you are not allowed to create a common denominator when dividing fractions. Why? Because my teacher said so. Now, in teacher's college my teacher is stating that you CAN use common denominators to divide fractions.

Heitin, Liana. Education Week. With Fractions, Common-Core Training Goes Beyond 'Invert and Multiply' (August 12 2014). Math, [Online Image]. Retrieved From http://blogs.edweek.org/edweek/curriculum/2014/08/fractions-common-core-invert-and-multiply.html

For example: 5/6 divided by 1/3 -find the common denominator: 18 is a common denominator.
HOW did we get that you might ask? Well both 6 and 3 can be multiplied by each other to get 18. Thus, whatever you do to the denominators you must do to the numerators.
So, 5/6: 5x3=15 and 6x3=18. Now our fraction becomes 15/18.
So, 1/3: 1x6=6 and 3x6=18. Now our fraction becomes 6/18.
So, 15/18 divided by 6/18= 15/6/1 a three part fraction which = 15/6/1 because both denominators being 18 can be divided by each other, equalling 1. We drop the 1 and this fraction, 15/6 can be simplified by dividing both the numerator and denominator by 3. Thus, giving us 5/2 as the simplified answer.

One more example using the common denominator method:
4 divided by 2/3... How can we solve this? - We must find a common denominator. I choose 3.
Therefore, whatever we do to the bottom we must do to the top. So I multiply the numerator 4, by 3 = 12. Thus, my equation becomes: 12/3 divided by 2/3 = 6/1. This can be simplified to 6.

Wiki How. How to Divide Fractions by a Whole Number. Math, [Online Image] Retrieved From http://www.wikihow.com/Divide-Fractions-by-a-Whole-Number

HALLELUJAH!!! IT'S A MIRACLE

I find doing numerous examples helps me to remember the process for solving problems. Therefore, making me more successful when answering math questions. For me it's all about repetition.

Here is a fun link that I learned about from my math lesson, the object of the game is to answer the questions using your fraction skills to make several smoothie recipes.

http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.FRA&lesson=html/object_interactives/fractions/use_it.html

Rules to take away from this lesson:
-Yes you can divide fractions without inverting them. Just simply divide across.
-Yes you can use a common denominator to divide fractions- why the hell not?
-When creating a problem make sure it has a wide base= scenario where everyone can get started
-When creating a problem make sure it has a high ceiling= lots of choice in between, students can add onto the problem.

As a future teacher it is important to remember the, 6 Fail Safe Ways for Opening Problems:
1. Begin with the answer.
2. Ask for similarities and differences- How is multiplying fractions like dividing fractions? How are they different?
3. Leave certain information out of the problem. Ie. omit number's.
4. Provide several numbers and math words so the student can create a sentence using all of them.
5. Use soft language, Ie. Two fractions are almost but not quite equal, what could they be? Example: 3/4 and 8/9.
6. Ask to prove if an idea is true or false.

This past week we learned a lot in our math class. We learned the PROPER way to divide fractions by dividing across the fractions as well as, finding common denominators to divide the fractions. These are the appropriate methods that I will use when teaching my students to divide fractions. It is important to remember the take home rules and the 6 Fail Safe Ways for Opening Problems for your students.

Till next time,
Cheers, Courtney

Fun With Fractions! - Week 3

http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.FRA&lesson=html/video_interactives/fractions/fractionsSmall.html

This week's math class was all about FRACTIONS! Above is an introductory link to Fractions which was provided in our week 4 folder on Sakai. The video is short and sweet! It discusses how fractions are used in our everyday world such as in hotels and restaurants. Fractions are used through multiplication, division, subtraction and addition in order to keep a kitchen running smoothly. It is always important to show our students how math is used in the real world. This will avoid statements such as: "I'll never use this in my job." & "Why do I need to know this, it doesn't apply in the real world."

Our class this week started off with each student choosing a fraction that they found interesting. I chose 1/4 because this fraction can be related to money and measurements for baking. We were to model our fractions in as many ways as possible, state why this is a fraction, and what's important about it. Even though every student came up with different examples of a fraction, we all had similar definitions. For instance, a fraction has a numerator-the top number and a denominator- the bottom number. Both of these numbers are separated by a line, creating a fraction.

Furthermore, we learned that there are various types of fractions. There are proper fractions which are part of a fraction, unit fractions which are fractions with a 1 as the numerator, mixed fractions which have a whole number and then the fraction, ex. 1 1/2 and lastly, there are improper fractions in which the numerator is more than the denominator, ex. 25/5. We also learned that fractions can be added together and subtracted from one another. However, the fractions must have a common denominator. To find a common denominator we must find a number that both denominators can be multiplied to. Then we multiply the numerators by what the denominators were multiplied by.

For example: 2/3 + 5/8
Common denominator =24- How did we get that? We multiplied the first denominator, 3 by 8 and the second denominator, 8 by 3= 24. Therefore, what we do to the bottom has to be done to the top. So, the first numerator 2, would be multiplied by what it's denominator was multiplied by =8 and the same for the second fraction. Thus, 5 would by multiplied by 3.
Answer: 2/3 + 5/8
= 2/24 + 5/24 -denominators done
= 16/24 + 15/24 -numerators done
=31/24

Also, we can simplify fractions by finding a common number that can be divide by both the numerator and the denominator.
For example: 18/24 can be simplified by dividing both numbers by 6
Answer: 18 divided by 6 = 3 and 24 divided by 6= 4
Simplification: 3/4

Furthermore, every week we are encouraged to provide context and real-world applications to our teachings and problems in order to keep the students interested. This week, Pat taught part of her Fraction's lesson using The Hershey's Milk Chocolate Fractions Book. This book teaches parts of whole fractions to students. Pat provided each group with a 16 piece Hershey's chocolate bar. As she read the story we separated the chocolate bar into the various fractions stated in the book. This exercise was EXCELLENT! Every group had to work together in order to solve the problems, thus promoting collective learning. This activity is both fun and informative, it engages the students and makes them want to learn math! This is an excellent and tasty idea for a lesson that teaches Junior/Intermediate students the basics of Fractions.


Helt, Courtney. 2016

As well, Pat stressed the importance of manipulative's again this week. Manipulative's are extremely useful for a lesson involving fractions.

Helt, Courtney. 2016

As a class we experimented with the Hershey's Chocolate bar, egg cartons, various blocks, number lines and strips, clocks, as well as pie plates and cards from the student presentations. Each manipulative proved that fractions can be solved easily if we have something visual to work with.


As a future teacher I would highly encourage and recommend to my students the use of manipulative's, even if the students claim they do not need them. KIDS NEED MANIPULATIVE'S. NO CHOICE!
They provide a fun, engaging and collaborative learning environment for all students. 


Helt, Courtney. 2016

 

Consequently, this week was filled with manipulative's and that made learning about Fractions extremely fun! Teachers teach  through problem solving and visual aids help students to solve their problems. Below is a terrific link that Pat informed us about. Math Playground has numerous games and problem solving activities that students can complete for various units. I look forward to the coming weeks and what new teaching methods we will learn from Pat.

 

 

http://www.mathplayground.com/


Till next time,
Cheers, Courtney



Algorithms: Making Sense For All Students - Week 2

Last week's math class opened with the question, "Why encourage Alternative Algorithms?" When I heard this question I instantly put my head down because I did not understand the concept of an algorithm. I shyed away from the word because I thought it was something extremely complex and out of my mathematical league. However, to my surprise and embarrassment this big word, "algorithm", is simply a step by step process for how to solve a problem.

In my opinion, teachers MUST encourage alternative algorithms because not every student learns in the same way. Algorithms promote creative thinking for how to solve a problem. This thinking might be understood in numerous ways depending on the student. One way of solving a problem might make total sense to one student but another way might make even more sense to a different student. As a result, I believe in promoting a classroom that encourages my future students to learn in a way that best suits them. There is no need for one right solution because there are thousands of right solutions. It is the responsibility of each individual student to find that one, or multiple right ways that best suits their learning.

Below is an example of Skip Counting presented in last week's class. Skip Counting is an algorithm that uses a number line to solve addition and subtraction problems. When using a number line it is important to remember that the line always increases to the right and decreases to the left. Skip counting can be used for students in all grades. I love this method because it makes sense. I am an extremely visual learner and this method appeals to me because I can see the process it takes in order to get the answer. The use of a number line helps students to keep track and visualize their math problem.

Problem: (Nathan's class goal is to sell 50 tickets, they have already sold 332 in the first week, how many will they have to sell to meet their goal?) 500-332=168 The 332 is broken down into 300, 30 and 2 across the number line. Younger students could break down the 300 into (100, 100 and 100) to better visualize the skip counting.

Helt, Courtney. 2016

As well, this picture is taken from last weeks math class. Below is an example of how to solve a multiplication problem using the concept, objects in an array. This is one way for understanding multiplication. Again, being a visual learner this solution makes sense to me. The problem is separated into a rectangular chart. Students can break down the process of multiplication through sections to further their understanding.

The multiplication equation 25x 28 is broken down into 20 + 5 and 20 + 8. Each number is multiplied by the adjacent number and the totals are added together. Therefore the equation is further broken down, and expanded to provide insight into the equation.

Helt, Courtney. 2016

Furthermore, it is crucial as new teachers to understand the importance of teaching our students how to solve equations in numerous ways. It is also crucial to show our students visually what we are doing in order for them to fully understand there math problems. Providing students with open problems will encourage interest and creativity. This will keep our students wanting more from math!

Jo Boaler couldn't have put it more perfectly when describing, Brain Crossing and it's importance to learning math, "Drawing, and visualizing and using symbols together in math is the most powerful math learning." Hence,it is key as future teachers to provide students with multiple ways to solve a problem and encourage the use of visual solutions.

https://www.youtube.com/watch?v=qZBjub36Bvs
Boaler, Jo. [S Lamb] 2015, August 25. "Day 2 - Brain Crossing" Retrieved from https://youtu.be/qZBjub36Bvs

Till next time,
Cheers, Courtney