Summary and Comments on Battleground Schools

The view on mathematics education has varied between two politically linked ideas since the 1900’s.  The Progressive viewpoint focuses on a deeper level of understanding of mathematics by both the student and teacher.  It encourages teachers to take a lesser role and allow the students to take up more of the learning process.  The Conservative viewpoint focuses on teachers lecturing and students listening and copying notes rather than stimulating a deeper meaning of the content they are learning.

 The negative view of mathematics by parents, elementary teachers and teachers using the conservative method of teaching math have fueled three reform movements in mathematics: “Progressivist reform, the New Math and the Standards-based Math Wars”. (395)

 The Progressivist Reform in the early 1900’s focused on creating teachers who not only taught students how to achieve answers but also why the methods they used gave these answers.  It focused on involving the students in their learning rather than the common lecture method so as to create students who would become individual thinkers rather than followers.

 The New Math era of the 1960’s followed on the heels of the Cold war when competition with other nations became prevalent.  The New Math created by the SMSG, upon the anxieties of politicians, resulted in a curriculum stemming from university mathematics that many teachers and parents at the time knew nothing about.  The goal of this era was to create scientists and mathematicians without regard to those who may have not been interested.

 The Math Wars beginning in the 1990’s were battles between those we did and did not agree with the standards put in place in the school system by the NCTM.  When the TIMSS published their results comparing educational levels across different countries, opinions over who’s teaching methods worked better surfaced and the battle continues today.

 I was very interested to see that mathematics has been so political for so long.  It is interesting to see where our current curriculum stems from and where these ideas got their start.  I found that the Progressivist Reform is similar to what we as teacher candidates are experiencing now.  Our idea of lecturing and only teaching the how not the why is being challenged as we speak, similarly to the movement that occurred in the early to mid 1900’s.  I find it slightly upsetting that the New Math era really focused on creating students that would become adults that would rival other nations in scientific and mathematic knowledge. It seems that no thought went into the students well being and only what would benefit the politicians and make their country look good.  I really feel that there may be no end to the Math Wars that are continuing on today.  There are too many people with a vast array of opinions that have a say in the math curriculum today for anything to be resolved in a short amount of time.

Personal Response to Interview

When we fist began this assignment I really wanted to gain an understanding of what it is like to be a math teacher and how students feel about math in general.

 

Mr.Y gave us answers above and beyond what I was expecting hear.  I found his response about how to engage students with low motivation particularly interesting.  I have always felt that I as a teacher I would want to show students that math is fun and exciting but Mr. Y made me re-evaluate at which times I should use this enthusiasm.  Perhaps because there are so many students in our schools who have a math phobia I should be careful how I place this enthusiasm about math in the classroom.  Keeping an open mind and explaining to students who aren’t highly motivated that I understand that math is difficult and not always exciting may be the proper way to approach these situations. 

 

I found Mr. Y’s tip about making use of colleagues AND students to be highly interesting.  From this I realized that using brighter students to assist those who are having difficulties is not only a way to vary explanations but also a way to have students actively engaged in the classroom.  This is something we are constantly being asked to strive for in the teacher education program.

 

I highly appreciate the answers our student provided to our questions.  I found it interesting that the student we interviewed felt she would prefer to work alone rather than participate in group activities.  This was really the opposite answer I was expecting. 

I wish we had all had the chance to speak with Sam’s sister and some other students about our questions to get a more in depth look at how a student views math.

 

I enjoyed hearing some of the other questions that were asked to both students and teachers in class on Friday.  One group asked a question about whether students should have homework and how much, to both teachers and students.  I believe homework is important as and educator and I was surprised that most of the students interviewed in that group felt so as well.  I also found it interesting how the answer to this question varied so much in the teacher responses.  It really shows you how each person takes their own personality and ideas into the classroom.  Another group asked for tips to make the classroom more engaging and one teacher responded that we should act as a discussion leader and have the students to teach themselves.  I have been having some doubts about this method, which has been so frequently referred to by all of our instructors, so I found it encouraging knowing that there are teachers in the school system who are using it.  I really hope that I will be able to incorporate this style into my own teaching style in the future.

 

Group Summary of Interview

In order to have our entire group participate in a face-to-face interview with a math instructor we chose someone who was a previous high school math teacher, Mr, Y.   He worked in Trail BC, Burnaby as well as a correctional facility. We were able to gain some valuable information from a great 45 minute interview.  This is what we found out.

 

Teacher Questions

TQ1) What did you find to be your biggest challenges with your early teaching experiences?

Mr. Y found that classroom management was his biggest challenge.  He struggled with getting upset with his students and felt that he could simply work around the chatter rather than clamping down it.  He realized later in his teacher career that this was NOT the way to go about things.  He explained to us that to overcome this obstacle we should make our expectations as clear as possible so students know what is acceptable in the classroom.

 

TQ2) What accommodations have you made to help students with learning difficulties?

Mr. Y had experience working at Burnaby South, which worked in conjunction with the BC school for the deaf.  Having someone shadow him to sign or repeat what he was saying made him realize how fast he spoke and how important it is to work on your pacing.  He said he would have liked to have had more experience with severe ESL students.  His tip was to be patient, and mindful of student experiences and histories because “their problems usually have nothing to do with you.”   One particular example our group found memorable was Mr. Y’s story of a young boy he taught who seemed to just hate him and wanted nothing to do with his class.  It ended up that this boy had an abusive father of the same nationality as Mr. Y and so the association was negative thus showing us that we can’t take everything personally in this job.

 

TQ3) How do you engage students with low motivation?

Mr. Y answered this question quickly and simply, “Humour can break down barriers”.  Having a sense of humour seems to be key to having a class that will respond to you.  He also feels that it is important to acknowledge that math is not everyone’s favourite subject and we should not go into a class with the attitude that we think math is the most interesting subject in the world and we are going to make them absolutely love our class right off the bat.  He stressed that the main goal for students with low motivation is to get them to simply come to class and to do this we should take an interest in what they are interested in and teach to their level of understanding.

 

TQ4) How do you vary your topics/explanations when students have difficulty understanding?

Jokingly he began with “Slower and Louder”, but he later explained it comes with experience.  Mr. Y said that because of the curriculum, it is not always possible to find many different ways to explain things so everyone can understand.  He suggested making use of your colleagues, they may have an alternative way of explaining a topic.  Mr. Y also made an interesting suggestion, to use the brighter students in the class as they may have solved a problem in a way you didn’t think of that is easier for a student having trouble to understand.

 

TQ5) What do you enjoy most about teaching? Least?

Mr. Y explained to us that interactions with the kids he taught was the most and least enjoyable thing about teaching.  He said that forming relationships with them and watching them grow is amazing, however it is difficult to watch them leave and move to new phases of their lives.  He also does not like the ways certain topics are presented in the curriculum as well as the fact that the curriculum is sometimes unbalanced throughout the grade levels.  One positive thing he said that our group found humourous was that he enjoyed having less marking than teachers of other subject areas. 

 

Our group also developed five separate questions to ask a student.  Sam interviewed one of his sisters who is in grade 10 math.

 

Sister #4 interview

 

SQ1) Why do you think it’s important to teach math in school?

This seemed to be a difficult question to answer and may have ended up being an answer that she felt she was supposed to give.  Sister #4 said that math is important for future life and many careers.  Interestingly she also said that it is important as it helps to develop ‘reasoning power’.

 

SQ2) How do you develop your first impressions of a teacher?

Our student bases her opinion mainly on humour as well as the organiztion of the classroom.  She feels that the more organized a teacher is indicates strictness whereas a less organized teacher indicates a more relaxed teacher.

 

SQ3) Think of a math lesson that you found particularly memorable.  What made it unique?

In grade 7 our student had a class that was instructed by a student teacher.  When they learned about Pi the teacher came to school dressed as a chef and brought them apple pie.  This indicated to us that she really didn’t remember the actual lesson about Pi, just that it was a fun class because they got to eat apple pie!

 

SQ4) How would you feel about incorporating more group activities in Math class?

Initially the student had a negative reaction to this idea and said she prefers to work alone.  She said that explanations from other students usually just add to the confusion of her learning.  She did however find the idea of group projects appealing.

 

SQ5) What is a memorable, effective way that a teacher has helped you to understand a tricky concept.

In grade 8 our student had a math teacher who explained equation solving using a unique analogy involving negatives being bad and getting sent to the basement until they come out positive on the other side. An interesting concept.

Our group found that Mr.Y's responses to our questions gave us some interesting tips and ideas that we can be aware of and use for our future career as educators.  Our student interview gave us an unique insight into the mind of a math student.

Reflection on the Article 'Using Research to Analyze, Inform, and Assess Changes in Instruction' by Heather Robinson

 

            I really enjoyed Robinson’s article, she provided some good hard evidence to back up everything we have been learning about engaging students rather than lecturing to them.

            One point of the article I found intriguing was that as a teacher, Robinson had followed the curriculum and textbooks and had students that did very well on assignments and tests in the classroom.  What I found surprising was, that when it came time to take the final exam, even the students who excelled in the class failed them.   This example really shows that as a teacher you have to go above and beyond simple lectures and begin to engage and involve students in what you are teaching them. 

            I also enjoyed seeing the differences between exam questions Robinson used from her old style of teaching and new style.  I found it interesting to see that her style changed from simple, find the answer questions, to ones that had the students explain, describe and provide more information than just a numerical answer.  I found this comparison very useful and I can see from the two styles how one will have students reflecting on the knowledge they have learned rather that just memorizing a simple formula. 

            Robinson also used the Think-Pair-Share idea we have been learning about in our class studies.  I have been curious as to how you might use this in a math class setting and Robinson provided some great examples of how she used this technique in her own classroom. 

I found the Jigsaw approach discussed in this article so neat and exciting!  Who would have thought of having students become responsible for their own learning as a “topic expert” within a group and the teacher simply acting as a facilitator?  I have never thought of teaching a math class that way because I have never experienced that in my own educational experiences with math.  The positive implications of this method seem to be numberless, and I would be excited to try this method in my own classroom. 

            I found this article to be extremely helpful and motivating towards my own career as an educator.  I really found it useful to see the positive change in students’ learning  from a change in style of teaching by their instructor.  I plan to keep this article and hopefully use some of the ideas and tips it has provided me for my future teaching career.

Reflection of My Two Most Memorable Teachers

My most memorable high school teacher was able to convey everything she taught so clearly.  Her notes were organized, concise, and easy to understand.  When she marked assignments she never used 'x's only check marks which really created a positive atmosphere.  You could tell that she really cared about her students, she always stayed in her classroom during lunch hours to answer questions, help with homework and let students re-write or catch up on tests.  She was always positive and approachable which I appreciated because I always had trouble speaking with teachers.

My other memorable teacher was a also very friendly and approachable and willing to put in extra time to to help students out.  I was not a fan of his teaching style however.  He was a bit disorganized and a lot of times it would take me longer to figure out the lesson he was teaching us.  If you spent the extra time with him it would eventually make sense but it wasn't the clear concise teaching that my other teacher used.

I think that these two teachers have given me ideas of how i would and would not teach a class. My favourite teacher really informed me on how organization can be an important tool to my teaching practice.  This aspect of teaching really showed through in her lessons and exams.  In contrast my other instructor was not organized and I really noticed the difference when it came to understanding concepts.  I also learned that creating a positive environment and being prepared to spend extra time with students is very important and I would also carry this forward with my teaching practices as well.

Reflection of Microteaching Lesson

For my Mircroteaching lesson I was lucky enough to have a large group of 8 people to teach how to throw a frisbee and to be able to take them outside to practice.  

I was pleased that my peers found my lesson engaging and fun.  Many felt that the analogies I used were helpful when learning the techniques of the throws I taught them and appreciated learning how to perform the throw as well as when it would be used in a game setting.  Some of my peers already knew how to throw a frisbee but mentioned they enjoyed the pointers I gave them for improving their skills as well the use of Elaine, who did a similar lesson and was already skilled, in some of my demonstrations.  One of my peers suggested that next time I mix up the partners, putting a person with strong skills with a person with weak skills.  I had not considered this option and would definitely use it next time!

I have previously taught this lesson in another class but creating a proper lesson plan made the lesson go so much better.  I found I was able to get my points across with some of my analogies and I was pleasantly surprised at how quickly my peers who did not have prior knowledge of all the throws were able to pick up the techniques.  I liked that I planned well enough so I had time to go around and visit all my groups to see how their practicing was going. I think my pace for the time we had was good and by making a conscious effort to be loud enough for a larger group I think everyone was able to hear what I was saying.  Next time I would make better use of the people who already had prior knowledge of the throws I was teaching.  Having them help others, or possibly do a demonstration themselves would be a great way to have them more involved and not get bored.  

I had a great time with my peers and enjoyed teaching my lesson and participating in my peers lessons as well.

Microteaching Lesson Plan

Microteaching Lesson Plan

1.)Bridge- Show class my disk (Frisbee) and ask them if they have heard of the game Ultimate Frisbee.

 2.) Teaching Objectives- To have the students working together and being involved in a participatory activity. 

To develop the students Frisbee throwing skills.

 3.) Learning Objectives- Students will be able to throw a disk in three different ways, a)backhand

b)forehand

c)hammer throws

using the proper wrist and arm mechanics.

Students will learn when it is appropriate to use each of these throws in the game of Ultimate Frisbee.

 4.) Pretest- Has anyone ever thrown a disk before? 

Do you know the three main types of tosses?

 5.) Participatory- Each student will receive a disc. 

-As a group I will demonstrate the techniques of a particular throw and explain when to use it in a game setting. (backhand, forehand, hammer)

-I will then have the students repeat or show me the technique I have just taught them. 

-Students will then partner up and use one disc to practice tossing the particular throw to each other.

-I will repeat these steps with the other types of throws.

-If some students already know a particular throw we can improve on their techniques and those students knowledgeable can assist those students who don’t know the skill.

 6.) Post Test- What are the names of the three throws we learned today?

Give me a short demonstration of what each throw looks like and when to use it.

 7.) Summary-Today we have learned a backhand, forehand and hammer throw with a Frisbee, and know when to use them in the game. 

Next time we may improve on our technique and simulate a game setting to practice our three throws.

 

Skemp Article Commentary

            The article Relational Understanding and Instrumental Understanding brought forth many new ideas about the way I was previously taught and the way I may have taught math.  I recall in high school frequently being told to just use what I was given and not try to understand why things worked in class, so as not to become confused.  After reading this article I have begun to re-evaluate the way I may want to teach a math class and to give more thought to instrumental and relational understanding.  I have chosen some quotes from his article that I found particularly interesting or insightful to discuss.

            The first quotation “Instrumental understanding I would until recently not have regarded as understanding at all” (Skemp 2), I found surprising that someone would completely admonish one form of teaching over the other.  While I have begun to think relational understanding may have more importance I believe that the two of them can be used together to teach effectively.

            The next quotation I chose was, “there are two kinds of mathematical mis-matches which can occur.  1.  Pupils whose goal is to understand instrumentally, taught by a teacher who wants them to understand relationally.  2.  The other way about” (Skemp 4).  These mis-matches made me think that, as teachers, we need to remember that every child learns differently.  In order to effectively reach most of our students we should perhaps focus on using both types of understanding, instead of choosing one over the other, to try to avoid theses mis-matches.

            The third quotation says, “I now believe there are two effectively different subjects being taught under the same name, ‘mathematics’” (Skemp 6).  I found this quote hard to agree with, maybe because I am not as familiar or have not had as much time to think about the two types of understanding.  It is an interesting idea, but as of now I am leaning towards seeing them as different teaching styles that we must learn to use and not actual subjects.

            I found the next quote “Relational Knowledge can be effective as a goal in itself” (Skemp 10), and its subsequent explanation to be an exciting prospect.  If this form of understanding can be self-motivating to the student, math can become more enjoyable to them and we as teachers can be more successful in our jobs.  I would be interested in seeing how motivational or exactly what effects relational knowledge can have on a student or classroom.

The last quote I have chosen is “learning relational mathematics…can produce an unlimited number of plans for getting from any starting point within his schema to any finishing point” (Skemp 14).  I felt these words to be inspiring. As a future teacher, by using relational understanding, I could provide my students with the tools to rely less on me and allow them to have a more in depth knowledge of what they are learning.  I find it very interesting that this one type of understanding has the possibility to provide a student with an actual in depth understanding of their subject instead of memorization of formulas.

            I thoroughly enjoyed this article and how it made me evaluate the way I have taught mathematics and how I can improve on them in the future.  I will definitely try to incorporate both of the methods of understanding into my practice and learn more about relational understanding, which I am less familiar with.

References

1. Skemp, R.R.. “Relational Understanding and Instrumental Understanding.”First published in Mathematics Teaching 77 (1976) : 20-26