Fictional Letter from Future Students

Dear,
I wanted to let your know about a great math teacher I had in high school. She helped me see that math is easy and understandable.  Up until this grade I hated math and did not look forward to the semesters I had to take it. I probably began to dislike math when I wasn't doing well at it.  This teacher explained things in an understandable, simple and straightforward way.  She was able to bring this complex subject down to my level and not confuse us with details.  She was encouraging and caring because she often gave chances to redo some assessments to improve our mark.  She was very approachable and I felt comfortable admitting I didn't understand anything at all.  She was very patient and helped us see the answer for ourselves rather than just telling us how to do it.  Her lessons were fun and exciting because she didn't just talk at us.  We were all engaged and helping solve problems.  If I put my hand up to give an answer she never made me feel embarrassed if it was wrong.  
Regards.

Dear,
I wanted to let you know about a really bad math teacher I had in high school.  She confused me beyond belief and caused me to hate math for the rest of high school.  Her lessons were very confusing and all over the place.  She spoke to fast and didn't have time, or even know how, to properly answer student's questions.  The tests covered unexpected material which we hadn't become familiar with.  Her lessons were boring.  I would often space-out during her class because nothing was exciting.  She was often too busy to provide extra help and it was obvious she didn't put proper planning into her lessons.  
Regards.  

A few things I hope for is that I make my class fun and engaging where students want to get involved.  I don't necessarily want to only inspire my students in the area of math, but in life in general.  I want to be a positive role model for my students to believe in themselves and believe that they can do anything they want.  A few worries or fears that I have is that I will get stuck in a rut with my methods.  I worry that I will not be able to bring the subject matter down to their level.    

Battleground Schools: Mathematics Education - Article Response

While reading this article by Susan Gerofsky, I was surprised with the drastic changes which have taken place over the last one hundred years in the area of mathematics.  The Progressivist reform movement which took place around 1910 to 1940 was in response to the meaningless memorization procedures in the math curriculum during the late 19^th century.  The First World War brought about a need for people to be scientifically able.  Mathematics was brought to the front as an important subject area in the K-12 system.  This interesting because it seems that a major event needs to happen in order for the US to recognize they are lacking in a certain area to make a change. 

A similar situation also happened during the post-WW2 period when there was a fear that mathematics in the US was not keeping up with the rest of the world.  The response brought on The New Math during the 1960’s, and again seems to be a drastic change rather than slowly introducing and integrating new concepts and teaching methods into the system.  Adopting the polar opposite of what is already in place seems to never fully work.  Here, the government funded university mathematicians to write curricula, texts and teaching materials for the US and other nations.  It seems in this case, the drastic step was not well prepared. 

A simpler system was needed in response to the opposing debates and controversy over The New Math.  The Math Wars over the NCTM Standards from 1990’s to present time is the conservative response to the new progressive system.  The right-wing view is that teachers are experimenting and this is hindering the learning of their students.  I cannot help but wonder if a math curriculum can be developed which can include both a conservative and progressive approach.               

Assignment 1 Report

(Group Members: Michelle Davis, Hong Jiang and Nadine Lundie)


PART 1 – Mathematics Teacher

We chose to ask our five burning questions to two different math teachers with varying experience. The first teacher interviewed had graduated from the UBC four years ago and has been teaching grade 11 and 12 math. The second teacher is the Senior Math Expert and has 30 years of high school teaching experience. We decided to ask two teachers with different levels of teaching experience to compare our results.

We found the answers were quite different in that the responses from the recent UBC grad were responses that we as teacher candidates might have thought of. On the other hand, the responses from the experienced math teacher were quite different and her methods unexpected. For example, we asked both teachers how they approach both the students who like math and dislike math. The newer teacher said that when she has a student who is only there because it’s a requirement to graduate and they are not interested in pursuing anything mathematical after high school then she simply tells them what they need to pass. She explains the requirements for them to get a specific grade and lets the students decide for themselves what grade they want. The experienced math teacher did not bring up the notion of ‘requirement to graduate’ and said that she shows students that math is more than computation. She believes that math is a fine art and compares it to music in saying that playing scales is not all music is. She says that she teaches from the premise that math is creative, efficient, effective and fun.  She believes that all students can and should have an appreciation for mathematics even if they never plan to pursue it.  She is not content to just let them be.

This premise also relates to how she manages to relate math to concepts beyond the classroom. She describes math as a way of thinking which helps with organizational skills, efficient procedures and problem solving. She goes on to say that this mathematical way of thinking is used even for daily things such as your cell phone plan or relationship issues.  She firmly believes that math is more than just procedures to memorize and strives to make this come across to her students.

One thing our group found interesting was how the experienced teacher incorporated topics from the real world into the classroom compared to the newer teacher. Rather than presenting or telling about real world applications, the experienced teacher posed questions or problems for the students to think about. For example, using a parabola to represent a bridge or arch she would ask the students whether they could replicate a famous structure in a different location over another river of different width or to allow for taller boats. We found this very interesting because not only is she relating math to a real problem, she is also having the students try and solve it themselves. This would be a great idea for a group project. 

PART 2 – Mathematics Student

We asked our five burning questions to a high school student who likes math and a high school student who dislikes math. When considering math a mere subject, the student said that they like math because there is either a right answer or a wrong answer, and there is no maybe answers. The other student said they dislike math because they feel it is too hard for them to understand and they wait too long to ask for help until right before the unit test. Our group was wondering if perhaps the teacher was not approachable enough for extra help, or if the student already established a sense of defeat about math.

We found it interesting that the students had similar answers as to what about a specific math teacher made them their favourite. Both the students said that the teacher made math fun, used good humor and brought jokes about math into the lesson. For example, one of the students said that their teacher gave the three different forms for the equation of a line names that were funny and non-math related to help students remember. The student who disliked math said their favourite teacher explained things in the simplest and easiest way and the student who liked math said their favourite teacher did things that were hands on and interactive. One of the students also said their favourite teacher let them watch “Finding Nemo” during class.  It seems to us that it is much more about the relationship that the teacher built with the kids that made them memorable.

A few of the other comments we found interesting had little to do with the content of mathematics itself.  The student who likes math said that her teacher cared, wanted to help, and made sure that the students were doing okay, and not just in math. The student who dislikes math said that their favourite teacher had a positive attitude. We found this intriguing that these characteristics are completely unrelated to the subject. We have been learning that being a teacher is more than knowing and teaching your subject matter. It is also about caring for your students and their success.

Of course the issue of homework came up with both students.  They both said they did not much like homework, which is not surprising. The student who dislikes math said that if too many questions were assigned they would dread even getting started on it.  It’s an interesting issue; how much homework is too much?  How much is not enough?  As the teacher how do you treat homework in the evaluation process?

Conclusion

This interview was very eye opening for all the members in our group. We can relate to the answers from the newer math teacher, although we aspire to develop the methods of the experienced teacher. We believe the confidence and creativity this teacher brings to the classroom comes not only with experience but also with constant reflection and adaptation.

We gained a different perspective by interviewing both types of math students. We saw that they had different concerns in areas like what made learning the easiest, but they had the same ideas about homework and why a certain teacher were their favourite. We learned that the teacher having a positive attitude and caring about their personal wellbeing, which are both unrelated to math, are more important than we previously thought. 

Micro-Teaching Reflection

Every evaluation I received from piers said that they could identify all areas of the BOOPPPS lesson plan format.  I felt the hardest area to cover was the bridge, since we didn't know what would come right before my lesson.  I ended up relating my lesson to the one that finished right before and also gave a bit of background as to why I chose this topic.
All of the evaluations suggested different areas of development.  One was timing, because my teaching lesson didn't quite make it to 10 minutes.  I was expecting this suggestion because I felt that I rushed slightly through the lesson.  I had timed the lesson at home and it was 10 minutes but perhaps in front of a group the pace tends to speed up.  Another suggestion was to take into account that certain positions require flexibility that some students didn't have.  The third suggestion was to perhaps give individual feedback to each person while they are attempting the positions and give adjustments.  The last suggestion I recieved was to perhaps take the lesson further and teach ballet movements rather than just positions.  All of these suggestions were great because they were things I did not think of, especially giving individual adjustments and help.  Another improvement I would like to develop is incorporating more humor into lessons.  
All the evaluations highlighted that one of the lessons strengths was the post-test I did with candy as a prize.  I too was expecting this to be unique to my lesson.  
   

   

Micro-Teaching Lesson Plan

BRIDGE

WHAT-  Link my micro-lesson to the previous student's lesson.  Introducing what my lesson is about and why I chose it.  I took ballet many many years ago and this is one thing I have never forgotten.  To get started I will have everyone put on their "pretend tutus".

TIME-  2 minutes

MATERIALS-  Adequate space to spread out and our "pretend tutus"

LEARNING OBJECTIVES/OUTCOME

WHAT-  Students will know the five ballet positions and be able to demonstrate them.  

TIME-  n/a

MATERIALS-  a great micro-lesson.  

TEACHING OBJECTIVES/OUTCOME

WHAT-  The objective is to engage everyone and for them to see that ballet is easy!  I have the personal teaching objective of developing clear communication and easy to follow instructions.  I must watch that I don't talk too fast or go too quickly.

TIME-  n/a

MATERIALS-  The "pretend tutus" might help them relax and have fun which may bring them to want to participate more.

PRE-TEST

WHAT-  Has anyone ever been to see a ballet? and which ones?  Has anyone ever done ballet? Any other kind of dance?  Can you demonstrate a positions which comes to mind when you think about ballet?

TIME-  1 minute

MATERIALS-  none

PARTICIPATORY LEARNING

WHAT-  First, "ballet hands", soft elbows and posture.  Then I will go through the five positions first with them watching, and the second and third time through they will participate.  Lastly, once through from fifth to first position.    

TIME-  3 minutes

MATERIALS-  listening ears and watching eyes.

POST-TEST

WHAT-  Mini quiz: have students close their eyes, get into the position I say and have them open their eyes to check with other students.  

TIME-  1 minute

MATERIALS-  prize candy

SUMMARY/CLOSING

WHAT-  Give them ideas about how they can use their new skill- teach friends, show family, job interviews or even audition for a ballet company if you don't succeed at teaching.  And remember to take off your tutus and give them back to your ballet teacher!

TIME-  2 minutes

MATERIALS-  none

          

       

Dave Hewitt Video

I thought that Dave Hewitt's teaching methods were fantastic.  He developed the students mental math before he went into the visual aspect of it.  I think that he made the math less intimidating by saying it out loud and having them work it out in their head first.  I feel that if he would have written the equation on the board first and then explained the notation the students would have had a harder time connecting the it to the meaning.  I would definitely try to use these methods in my classroom.  I think the hardest part for me would be resisting the urge to say whether their response is correct or incorrect, because that's what the students are looking for.  In having the students figure out for themselves whether they have the right answer or not will help them develop confidence in their abilities.  

Remembering my Math Teachers...

In grade 7 I really began to enjoy math more than my other subjects.  My teacher was Mr. P and he was great.  I don't remember thinking it at the time, but I realized how good he was after I had another teacher for the next two years.  Mr. P's teaching method was very organized and simple.  He introduced a new concept with the minimum and didn't get carried away with details, applications or extensions of the idea.  Once the concept was introduced he would elaborate.  I remember him drawing a number line and moving along the line when he wanted to show addition and subtraction of negative numbers.  These visuals he used were very helpful to me.   What I learned from Mr. P is that in some areas of teaching math less is actually more. 

The next two years I had Mr. T and his methods were quite different from Mr. P.  He was great at math but had a difficult time explaining it in any other way than his own.  Many of my classmates were confused and he had a hard time clarifying their confusions and answering their questions.  I often helped my friends in class and I remember saying 'ignore all this and just focus on this...' because he presented so much material beyond the scope of the course that it confused many students.  He thought it would make more sense to students to go beyond the concept and introduce the extension thinking that would help the students to make sense of it.  But all it did was puzzle them because they were not  yet at that level of math to understand what he was even talking about. 

One more think about Mr. T, he must have mixed me up with another student on parent-teacher night because he told my parents all about how I was struggling and needed to do more homework to bring my mark up.  It was quite embarrassing. 

Reflections on In-Class Fraction Exercise

I thought that this activity displayed relational understanding vs. instrumental understanding perfectly.  By drawing circles and dividing them into groups or cutting each one up like a pie can really help students see what they are actually doing.  I am looking forward to finding ways to teach each topic like this.  

Assignment 1 Questions

Questions for the Math Student:


1.  What memorable method did a current or previous math teacher use that made the learning easier?
2.  What memorable method did a current or previous math teacher use that made the learning fun?
3.  Why is your favourite math teacher your favourite? What did they do differently than other math teachers?
4.  Why do you like (or dislike) math?
5.  How do you feel about the amount of math homework that you get?


Questions for the Math Teacher:


1. How do you incorporate topics into your math class which show how the math applied to real life outside the classroom?
2.  Do you include history of math into your classroom? How?
3.  What types of methods do you use to ensure that the student’s homework or assignments are
their own?
4.  What is the most challenging part about teaching the subject?
5.  How do you approach both the students who like math and students who dislike math?

Skemp Article Response

Through reading Skemp’s article Relational Understanding and Instrumental Understanding I have come to look at my days spent in math class in high school with a new light.    

                I often helped other students with their math and would be frustrated that the teacher would teach “beyond” or “above” the subject matter which confused the students who were struggling. However, I now see this would not have helped students when they encountered a slightly altered problem.  

               While I was in class much of the relational understanding concepts went right over my head.  I was only concerned with the instrumental understanding because that was all I needed to complete the assigned homework.  I usually understood the concept instrumentally at first, and then at a later time when I studied that material on my own I would come to understand it relationally.  I would see the larger picture and make sense of the material from class.

                I can see the teaching dilemma which is to teach for those students who have a difficult time relationally understanding the concepts.  It is tempting to resort to teaching for instrumental understanding to achieve higher examination scores.