Math 9 Project and Rubric

Lesson Plans - Math 9

Grade 9 - Unit Plan Algebra

Math Problem From Text

Practicum Experiences Reflection

When reading my first partners responses I realized that there were some distinct similarities and differences. Both of us found that students in general where well behaved and respectful. Both myself and my partner found that there was no strict policy on the use of ipds and phones, I personally find this very troublesome as we may struggle to change implement a policy. The same applies to the lack of consistency for punishment of lateness. I found that in both math and PE there was great communication between teachers which is in contrast to what my partner saw. At times in PE facilities were shared due to weather, and in math collaboration was used to write midterms. I was amazed to read on my partners blog that there teachers could not deduct marks for late assignments, where as I thought I saw students recieve zero for work not completed and no opportunity to hand it in late.

It seemed that my second partner had a sort of a shock when entering the classroom. It appeares as though the students were well below his expectations. I feel it is important to set high standards for students, and we are tools for the students to use to get to these high standards. Once again this partner saw a lack of communication between teachers, especially outside of departments. I think that it is essentially a school atmosphere that effects this as all teachers were really welcoming and seemed to communinicate well between departments. However, as my partner noticed it is clear that some students/parents want to try to struggle through principles of math instead of being placed in one of the alternate choices. At my school a student was taking principles of math 10 for the thrid time and still not passing!

Thinking Mathematically

Chapter 2 in the text provided us with an interesting way of examining problems in math. I feel that I was in fact following a format similar to the one presented, but not in such a formal way. The text book provided us with a three step technique in solving problems. The first step, is the Entry Phase, here the student is to carefully read the problem to try to grasp a better understanding for the problem. The text recomends three questions in order to facilitate the Entry Phase; (1) What do I KNOW? (2) What do I WANT? (3) What can I INTRODUCE? using these three questions should help lay the framework for the next step. The next step is the Attack Phase, this is the stage through which you feel that the problem has become your own, and the problem is either abandoned or resolved. The third stage is the Review Phase, here one should review their work. There are three aspects to the Review Phase: (1) CHECK the resolution (2) REFLECT on the key ideas and key moments (3) EXPAND to a wider context.

Chapter 3 refers to the responses to the state in which the individual has a feeling of being STUCK! This feeling in my opinion can act as both a positive and a negative depending on each individual. Some might interepret being STUCK! as a motivator while others may find it frustrating and give up. But just as stated in the text I believe that this phase should provide easch student with some sort of learning. There can also be the great sense of accomplishment from this phase which I would think is similar to the AHA! response.

There is one aspect of the two chapters that stood out to me which we need to be aware of. As much as me might believe that every child should love math or should enjoy math it is just not going to happen, just as not all students enyoy PE or English or Biology and so on. The textbook refers to taking math problems as a chef would take tasting food, in that a chef would savor the flavor. In this context yes a chef would savor that flavor but would a dentist or a math teacher, so it is difficult to ask everyone to look at math the same.

Reponse to Practicum

During my practicum I was actually surprised with how good the students were. I was expecting to have some students that would be troublesome or disruptive in the classroom, however, most if not all students were very respectable in the classroom, especially the math classroom compared to a PE class. However, in all this I also learned that as nice or well behaved a student maybe in the classroom we still need to be aware of how he or she behaves outside of school. We had an incident at school where students that appeared to be very respectful in class, were far from that when removed from the school setting. If we learn more about these students we may be able to affect how they behave outside school hours.

In the PE classes I was somewhat surprised with the lack of lesson planning that the teachers actually did. A major reason for this was that teachers were unaware of their facility for that week until Monday morning. This was a learning experience for me, in that it showed me how to think on my feet and develop a lesson quickly that serves a purpose to the student.

In my math classes, I was surprised by how little lecturing was actually done. Typically the teacher would lecture for no more than 20 minutes and then allow the students to do text book work. I can see the positives in this, I think that allowing the students so much time to do their work and communicate with one another also allows them to teach each other. With this technique students learn both from another student and also learn by teaching their peers.

I also learned that students will respect fair and understanding teachers. Teachers that are fair to their students and cared for the student seemed to have a better understanding between themselves and the student. Students enjoy being treated fairly, and not being treated as someone underneath the teacher.

Evaluations

Response to Teaching Lesson

I think it is important to teach students as to why rules are such. Simply telling students that you cannot divide by zero is not an effective way of teaching. The lesson plan was effective because it allowed students to link together different concepts learned, possibly in a previous lesson or previous grade. The lesson also incorporated different teaching styles. There was an explanation displayed on the board, this is effective for students that need concrete examples for learning. This form of teaching let students learn through breaking down examples. Furthermore, added to the lesson were the verbal cues provided by the teacher, this will help students who learn better through auditory senses to gain knowledge of the concept. The aspect that I really like was the second form of teaching, graphically. This way of teaching allowed for students who didn’t quite understand from the first analytical style another chance to grasp the same material. Just as displayed in this micro lesson, I think it is vital to provide students with many opportunities to learn, through many different teaching methods. It is important to give students many opportunities to be engaged by math, as not all students learn through the same styles. To extend this lesson I would possibly set it up so students work together to build a story to present to the class about dividing by zero.

Poem

What is zero?

I am zero, but what does this mean?
Am I nothing, irrelevant and empty?
Do you consider me to positive, negative or neither?
Or is zero even a number at all?

I am zero, but what does this mean?
I am the score at the start of every soccer game.
I am the point at which water will freeze.
There is no distance between you and me.

I am zero, but what does this mean?
Divide by me and get no answer
Multiply by me and always get the same answer
I am zero, so many uses you’ll see.

Free writing - Divide and Zero

Divide

When thinking about the word “divide” the first thing that comes to my head is division. I think about splitting things up, as in dividing a PE class into four teams. I’m sure the word divide can be taken into many contexts and now that I think about I’m sure that a form of the word divide is used in everyday of my life. Our classes at UBC are sometimes divided into two or three classes throughout the week. My day is divided in many ways as well, there is the time I spent at home and the time I spend at school, the time I spend travelling between the two, all of those aspects divide up parts of my day. Thus far the way I have talked about the word divide has been a view in which something is taken and split up into smaller pieces, but what about when in school we divide by a number smaller than one we get a larger number.

Zero

When I first think of zero the number zero is what pops into my head. Then I start to think what value does zero have, does zero mean nothing? Why is zero not the freezing point in Fahrenheit degrees with respect to temperature yet it is when using degrees Celsius. Zero is what is used as an initial value in most sports, games typically start with score 0-0. But why zero, and why is it called zero. My whole life I have learned that zero is essentially zero. There has been no explanation really as to what zero is and what zero means. Zero could possibly be seen as the most important number, because it acts as the starting value for so many situations.

Citizenship Article Response

From the article I took that it is important for us as math teachers to teach for learning outside the classroom. Math is essential in everyday life, no matter where you go and what you do there is typically some form of math in our world. It is essential that we teach students that they can apply the knowledge they gain in class and apply it to their everyday lives. From my days in high school, I remember that math was typically viewed as a boring class, based solely on lecture notes. I feel that if we give the students the ability to apply math to their own worlds they will be more easily receptive to math. With this in mind we must also remember that we are still obliged to fulfill prescribed learning outcomes. However, I recall from my interview with a math teacher that he feels that he now has more creative ability with the in the math provincial, as it is now optional. My other subject in education is physical education; here we discuss providing students with skills that will lead to healthy living and providing it in such a way that students will be able to apply these skills for their whole life outside of school. Math must be taken in the same context in my eyes. Math is probably the most prominent subject that can be used daily along with physical education. When we drive we need to know what speed limits mean, we need to know how much change we should receive, we need to be able to tell time. Management of numbers is vital in everyday life and we need to realize this in our society, as I am sure that the other twenty six students in this class know this, but not everyone else sees this.

Lesson Plan

Teaching objectives
To teach ‘equivalent fractions’ in a more ‘engaging’ manner.

Learning Objectives
The students will be able to recognize some fractions that have equivalent values.
Students will be able to add fractions with common denominators.
Students will have an opportunity to consider adding fractions with different denominators by first changing one or both fractions to equivalent fractions.

Bridge
Today we are doing jigsaws. But instead of pictures we are going to be using fractions.

Explain FREEZE including perhaps allowing which ever half of the class wins freeze most often, gets to leave first at the end of class.
Pretest
5 mins

Hand out sheet – 12ths, 6ths, already on. Ask students to complete outlines for 4ths, 3rds & halves and give an example on the whiteboard. They can then colour them in with pencil crayons not markers FREEZE –we would ask students to colour in the new bits that they have drawn on the sheets to make them feel more attached to it but you guys aren’t going to get that chance.
As they are drawing these, hand out the blocks. Put them loose on one table, in bags on another table with instructions not to touch and no blocks on the other tables. FREEZE you will notice that we have put some blocks on the tables. You need to consider very carefully when exactly you want the students to have access to manipulatives. See what’s happened here.
Once most of the students have finished drawing, ask them for their attention. Freeze – it is very hard to stop students doing something part way through so you may want to give both instructions 1 and 2 at the beginning. However, if you are stopping them, you may well want to do something like ask them to turn around to face you and fold their arms to reduce the temptation to carry on drawing while you are talking. If any of you here tonight draw while we’re talking you’ll get your knuckles rapped with a ruler!
Put a few simple fractions on the board and ask students to find some equivalent fractions, using blocks and fraction sheet to help, and ask them to put their hands up to offer their answers.

Activity
10 mins

We are going to do fraction jigsaws. You will each have a jigsaw of your own to complete but you can work together in groups of two or three if you wish. FREEZE - If the teacher continues talking now you will not have the attention of many of the students because they will be figuring out their groups of three. So either, say “You can collaborate in groups of two or three so let’s sort out those groups now and you can move to be close to the others in you group” OR don’t mention groups until you have explained everything else. There are also many ways to arrange groups so you may wish to employ a particular method in this situation in the classroom, but tonight you can just choose yourselves.
Please choose groups of three now and sit with your group.

The finished jigsaw will look like this (overhead of blank completed jigsaw)
Except each white space will have a fraction or a fraction sum on it.
Adjoining pieces must have the same value.
Use the sheet and blocks to help if you wish.

Please finish your drawings and then try to complete the jigsaw. You probably won’t complete it today but you will have time again next lesson (you may wish to number the pieces you have completed before you dismantle it at the end of this lesson)
Hand out jigsaws. Put student’s names on their baggies.

While the students are completing this activity, consider the following
Possible hints:
· Count the number of pieces in the puzzle. What will the dimensions of the finished jigsaw be?
· Some people find it easiest to complete the edges first.
Possible questions:
How did you start with this puzzle?
At what stage did it get hard?
How did you get through that block?
How could it be made harder?

Post test
Ongoing

The post test will be completed during the activity by observing individuals and groups as they are completing the jigsaw.


Resources
Sheet of squared paper with 12ths and 6ths marked on for each student.
15 rulers and pencils
15 sets of blocks in plastic bags (6, 4, 3, 2 cm)
15 jigsaws in plastic bags
Permanent marker.
Overhead projector
Image of blank completed jigsaw
Whiteboard pens

Summary
In addition to completing the jigsaws in the next lesson there are a number of possible extensions.
These include:
Asking students to create jigsaws of their own while considering these questions:
· Would it have been harder if the numbers did not have to be "the right way up"?
· What if the same answer occurred more than once?
· What if there were calculations on the outside edges, rather than grey?
· Can you make a harder (but still possible) puzzle?

My Reflection on Assignment #1

I was slightly caught off guard by the fact that our student seems to have a positive view on math. I was honestly expecting a student at such a young age to be somewhat against math. However, our student enjoyed math and understood that the subject can be applied outside the four walls of the classroom. The student is an extremely focused student making it easy for her to shut out distractions in the class. It is important to remember that the student we interviewed is only entering her second year of secondary school math, so thus far she has only be exposed to one high school level math teacher.

I was extremely impressed with our student’s enthusiasm about math, and she seems like a student that you would enjoy teaching. She enjoys learning through the traditional lecture style of teaching as she can take home her notes to reflect on. As teachers we need to realize that not all students will learn best like this, and it is important to work with students in a way where all can be successful. Our student is able to see the connection with math in everyday life, and told us that she uses math outside the class for example when shopping or cooking. I think that this interview showed us that students do not necessarily come into your class with a dislike for math but may develop it through poor experiences in the class.

We ended up interviewing two teachers but there were some distinct similarities and differences in the answers provided by both. I found it interesting that both teachers told us that they primarily lecture, but do attempt to use other collaborative methods for the students. However, you could tell that one of the teachers felt slightly limited at times due to provincial testing but noted that this is changing because the provincial exam is now optional. I would have seem myself in a similar position in that I would have felt as though I had to teach to the test and did not want to jeopardize a student’s future. I think it is important to be inclusive to all students and both teachers understood the questions in different ways but both answers in my opinion need to be included. We must include the students with special needs and also include all students in general.

When assessing students both teachers mentioned tests and homework, but one left it at that while the other mentioned group work and other assessment tools. I think it is important that we use a wide variety of teaching styles, as not everyone will excel on a test where u get one chance. Furthermore, one teacher mentioned that at teams we as teachers need to be the student, I think this is important in that it will make students more comfortable and help us grow as teachers. When looking at the difficulties in teaching math we need to realize that at times it might be difficult to teach math and also at times it’s going to be hard on the students to relate concepts. It is important that we engage the class with fresh teaching methods; we don’t want students getting bored in class because all they do is expect the same thing to happen in every class. We also need to realize that students will have questions and I was told that a typical on is “when are we going to use this?", and that the way we answer this question will tell the students a lot about what we think of the material. So I think it is important that we have a passion for the subject and more so a passion for teaching all of our students.

Another Teacher Response

I also sent out our questions to another teacher, this teacher is a male math teacher in Surrey.
What kind of teaching style do you use?
I primarily use lecture type, especially with senior classes 10-12, however, with the junior classes you have more flexibility to do collaborative learning. In grade 10 and grade 12, I must prepare the student for the provinical exam, however, with the grade 12 exam now optional, I believe that there are various other activities I can promote within the classroom to elaborate on the curriculum.
What do you do to ensure that your classroom is an inclusive one?
Select different students to answer questions, use the entire classroom so that no one feels left out, students help create evaluation scheme for semester/term
If you lose control of a class how do you regain control?
I believe that the your first interaction determines how you manage a classroom. It is within your first interactions with students that you must present your expectations and outline any rules, policies and procedures that you have for them. And then be consistent.
How do you assess your students and in which ways?
Tests, quizzes, homework checks, group assignments, student teaching (get them to illustrate how they do problems on the board - you become a student)
What is the most challenging part of teaching math?
To relate how Math connects with realworld situations. You need to be prepared to deal with the question "when are we going to use this?" How you decide to answer this question, informs the students about your passion for the subject matter.

Peer Feedback

Peer Feedback

Summary of Student/Teacher Questions

STUDENT:
The student our group interviewed has just started her second year in high school, located in Victoria, BC. She has recently started a job and recognizes that the math skills that she has learned in the classroom carry over into every day tasks. When dealing with money she uses her knowledge of decimals, percents, fractions, etc. She is aware when her basic math skills are used in every day situations. Because of this, the student knows that learning math skills in school is important for everyone, regardless of how far they extend their math education. Although she can find math frustrating when new concepts are introduced, she is the type of student that persists and asks questions until she is comfortable with the material. The fact that she enjoys math class helps her work towards a better understanding. We have discusses many forms of teaching and learning for the students in a classroom but this student prefers reflecting on her notes at the end of the day. She feels it important to have a hard copy of what the important concepts were that she learned that day. She realizes that auditory learning is not always for her, so she accommodates by organizing her notes. She is very focused in the classroom and doesn’t let her surroundings distract her. This is useful for her learning style as she relies on her memory to help her connect concepts taught from class to class.

TEACHER:
1) What kind of teaching style do you follow?
I lecture the basics and until the required lesson has been taught, but then I initiate group work, projects, collaboration, peer-peer helping. I try to get the kids as hands-on as possible. I taught shop class for a long time, and you don't learn how to make something by watching, so they have to actually practice. they have to ask questions and think critically, which doesn't happen as often in a lecture-based environment.
2) What do you do to ensure that your classroom is an inclusive one?
It’s important to read files that accompany students with special needs. The first step is to understand your students and figure out how they are going to learn best. Then it's just a matter of facilitating an environment that is conducive to those needs. Utilize support works - that's what they're there for. And obviously, be an example; be accepting of all races, sexualities, cultures. It comes down to the golden rule, treat others as you'd want to be treated.
3) How do you regain control of a class after you've lost control?
Establish authority among your students from day one. Create a respectful environment; respect your students and students will usually reciprocate that respect. Deal with difficult kids one to one as much as possible, rather than singling them out among their classmates, which can escalate a situation. Physically move over to a loud area; you don't even have to say anything a lot of the time.
4) How do you assess students and in which ways?
Mathematics is different from a lot of other subject areas. There isn’t much room for points with creativity, inventiveness, or effort; the students have to know what is taught in the curriculum. 90% of the grade in my math class is from written examinations, and only 10% comes from homework. It sounds unreasonable to some, but I think its good preparation for university, where you have 50% finals. We have lots of quizzes thrown in, so all the weight isn't on their end exam.
5) What is the most challenging part of teaching math?
Keeping the subject fresh and interesting and relevant is important. It’s so easy to be lazy and stand up in front of the class and lecture straight out of the text. But in order to challenge students of all abilities, you have to make the classroom a community in such a way that if a few people are failing, the whole group is weaker for it. You have to get everyone involved and active, which takes a lot of effort.

TPI Results and Reflection

Gary Atwal here are your TPI scores:
Transmission total: (Tr) 31.00B=11; I=10; A=10
Apprenticeship total: (Ap) 36.00B=11; I=13; A=12
Developmental total: (Dv) 35.00B=10; I=13; A=12
Nurturance total: (Nu) 38.00B=13; I=14; A=11
Social Reform total: (SR) 30.00B=11; I=9; A=10
Beliefs total: (B) 56.00
Intention total: (I) 59.00
Action total: (A) 55.00
Mean: (M) 34.00
Standard Deviation: (SD) 3.03
HiT: (HiT) 37.00
LoT: (LoT) 31.00
Overall Total: (T) 170.00

For this test I scored high in the nurturance, apprenticeship and developmental categories. I agree with the findings because I believe this is the type of teacher I strive to be. Having had experience in Human Kinetics which is part of the Faculty of Education, I have been learning about safe environments and inclusive teaching. I want to be able to provide both of those for my students. I think that this test shows my intentions as a teacher, and I feel that the scores are somewhat accurate.

Assignment 1 - Questions

5 Questions for Student:

1. Can you apply what you learn in math outside the classroom?
2. Why do you think we need math?
3. Is there anything about math that intimidates you?
4. What is you preferred learning style?
5. What do you remember most about math class?

5 Questions for Teacher:

1. What kind of teaching style do you use?
2. What do you do to ensure that your classroom is an inclusive one?
3. If you lose control of a class how do you regain control?
4. How do you assess your students and in which ways?
5. What is the most challenging part of teaching math?

Response to Article

I feel that as math teachers more so than any other subject we need to work harder to engage the minds of your students. Many students look at math in a negative due to past experiences, thus we must try to bring them back to math. Different styles of teaching will engage students to learn more and participate in class with greater enthusiasm. I also think it is important to teach our students with understanding and not just turn them into robots; we need to teach them skills that they can use further in life. Furthermore it is essential that students do not just memorize formulas but implement techniques and strategies that can be used in different situations and adapted outside of the school setting.
Different teaching styles will enable to students to be more active in learning. If we allow students to teach one another, we will also encourage student development within the social aspect of life, as students will be interacting with each other. Also learning from other students allows students to see different styles and relate to one another.

Email Convo Between Two Past Students - 2 Letters Part 2

Hi Tom,
Nice hearing from you again, I hope all is well. Anyways, I remember Mr. Atwal as well, but for a different reason than yours. Mr. Atwal seemed to enjoy teaching and wanted to use different activities to make sure the classroom didn’t get stale. I liked the way he taught, he taught us techniques that we could apply to our lives and I still use some of them! If it wasn’t for all those “silly” activities that the PE teacher provided us with I don’t know if I would have passed the course. It was so much easier to learn from peers and ask them questions without feeling stupid. I was getting bored of those old math teachers just lecturing and testing, and usually with a scantron so they didn’t have to mark it. Mr. Atwal realized that not all people learn the same and not all can excel at writing tests so he provided us with many avenues for learning and assessment. Just my thoughts, talk to you soon. John

Email Convo Between Two Past Students - 2 Letters Part 1

Hey John,
I was just thinking back to the good old days of high school, where life was easy. And I started thinking about which classes I struggled in. Remember Mr. Atwal, I really couldn’t understand where he was coming from when he taught math. It was like they just stuck a PE teacher in a math classroom. All those activities that he had us do were pointless, like seriously just lecture and let me learn it for the test. All that group work threw me off because I would just sit there and watch all the other kids do the work and then throw my name on it. I still passed the course, but it just seemed like a waste of time with all his activities and different types of testing. Why couldn’t he just be the conventional math teacher that we have been used to here is the lecture here is the test its simple really.

Tom

Greatest Teaching Hopes

My greatest hopes for myself as a teacher firstly are that I can motivate the students to enjoy math. I wasn’t to provide the students with an environment where they enjoy coming to class. I want to encourage students to think for themselves and develop their own thoughts. Furthermore, I want to challenge students, I never want my students to be content with where they are; I want to challenge them to push them further. Finally I also want to teach in a variety of techniques, I don’t want the students coming to class with the expectations of being bored.

My greatest concerns are that my students are going to have previous negative view of the subject and not get interested in what is being taught. I am also concerned that with the new teaching styles being implemented, whether some students would shut them out and not grasp the concept or the “bigger picture”.

Micro Teaching Self Reflection

During my micro teaching lesson I thought that my progressions and steps in learning went well. I believe I was well organized and for the most part spoke in a clear and understandable voice. I also feel that I was able to use good eye contact when speaking to the others. I also think that the use of a mini lecture, and then bringing in props for the students to touch and use hit various learning styles.

If I were to teach this lesson again I think that I would come more prepared I feel that I was reading off my lesson plans and notes to much. I think that I would also try to engage more students through questions, because although I was asking questions they seemed to be dominated by one or two students so I think it’s important to work harder in involving all students.

I took the micro teaching lesson as a lesson where lack of previous knowledge was done, so I would expect to score low in bridging to prior knowledge as this was an independent lesson. The only comment made about development was with regards to timing. I finished my lesson with about one minute left so with some additional planning I am sure I could have filled the entire ten minutes as I did have other activities in mind when planning.

Memorable Math Teachers

My most memorable math teacher would have to be Mr. Mosely, at Tamanawis Secondary School. When you went to his class you knew that you weren’t going too bored by some boring math lecture. His class was typically based on lectures from himself, which is only one teaching style. However, in my times in high school this seemed like the typical and common practice. Mr. Mosely did however keep is lectures engaging, which some teachers were unable to do. He had a sense of humor which about 10 years ago was lacking in a math class. To say his class was only based on lectures is not totally fair to him as well, he was not like a drill sergeant in that nobody could talk and he expected complete silence. After finishing his lesson he allowed students to work in partners and/or small groups on problems which would allow students to understand topics from different points of view. Mr. Mosely was a very open and understanding professor and he created a teaching environment that encouraged learning. He was always available to provide extra help to those in need of it and always put in time to help students.

Another memorable teacher for me was Mr. Nagra. Mr. Nagra had good intentions but really lacked the qualities of a professional teacher. His lessons were disorganized and choppy. There were times in the year where he would make massive mistakes during the lesson and needed students to essentially teach the class, this could be seen as another teaching style. However, it was not effective as students lost respect for the teacher. I vividly remember Mr. Nagra creating his own formulas and techniques that would work for certain questions, however could not be applied universally, this was very frustrating.

Lesson Plan

How to Dress for the Outdoors

Objective:

• Students will be able to layer clothing to provide maximum protection against various weather conditions.

Lesson:

• Introduce Basics of Layering
  Ask students why we layer and how it is effective
  1 minute
• Introduce 3 Different Layering Levels
  Base layer, mid layer, outer layer
  Ask students for examples of each and of what would make a bad layer for that level
  4 minutes
• Go into specifics of outer different outer layers
  Wind resistance, waterproofing, insulated, rain wear
  Show examples – rain jacket, windproof jacket
  Ask questions that illustrate students' learning
  3 Minutes
• Activity
  Spill clothes on the ground and ask participants to develop an effective layering system from the provided clothing.
  Alternative:
  Split group into pairs and have one develop a good layering system and the other develop a poor layering system then justify their choices to the group – more individual learning
  2 minutes
  
  Total = 10 minutes
  

Equipment:

• Varying types of clothing
• Under armor/Adidas base layer
• Fleece
• Rain jacket
• Wind proof jacket
• Cotton shirts
• Cotton sweat pants
• Wind/water resistant pants
  

Safety:

• There should not be a concern with safety as most of the session is instruction through me and then a small activity from what was learned.
  The session does not involve any vigorous physical activity.
  

Conclusion:

• The activity at the end of the lesson will allow for the participants to demonstrate that they have in fact learned the basics to layering.
  Allowing the participants to develop a layering system will reinforce what they have learned.

Response - Relational and Instrumental Understanding

The article Relational Understanding and Instrumental Understanding by Richard R. Skemp looks at the two models of understanding with a bias towards rational thinking. After reading the article I found that I agree with the author’s position on the two methods of understanding. I think that teaching using a rational understanding method will benefit students over the long term. Although it is harder to teach using a rational understanding method, the overall end product of this type knowledge will allow for individuals to adapt to various situations.

Instrumental understanding is extremely limited to specific situations. Instrumental knowledge is very one way, and lacks the adaptability provided through rational understanding. Instrumental understanding is very direct and if implemented correctly should provide correct answers with minimal work. This technique provides formulas where one can simply plug in numbers; however, this limits the learner from understanding why those specific values are used. Instrumental understanding involves a lot of memorization of specific rules that can only be applied to one situation, thus a great amount of time and effort must be spent on specific topics.

In the end I feel that rational understanding, although more difficult to both teach and learn, provides the greater form knowledge due to the flexibility it provides. Instrumental understanding is simple and easy to teach and understand, however, the student does not learn as much as they actually memorize specific rules. In closing I feel that if we want our students to expand their knowledge base we need to implement more rational techniques of teaching.

Time Writing - Relational and Instrumental Thinking

Relational and instrumental understandings are two techniques which can be used when teaching students in all subjects. I think both methods could have benefits and should be collaborated in teaching. Relational understanding is making connections between concepts and learning through connections. This technique can be applied to math in that it allows the student to learn and transfer previous knowledge to a new subject. Instrumental understanding is using algorithmic thinking to understand and compute problems. Instrumental understanding is more direct and to the point, using algorithms to solve specific problems. To use this technique we can implement specific rules and tips in order to make understanding easier, an example of this is using acronyms to help remind us of mathematical rules.