Teacher collaboration in my school

Teacher collaboration is referenced in this week's discussion forum. Boaler (2006) states that teachers report collaboration to be critical to students' high level of achievement.

I believe that teacher collaboration is our best form of professional development and critical to student learning.

I work in a small one stream school where there are only 13 teachers. While it is not possible for us to collaborate at grade level, we do participate in staff collaboration as a means of sharing best teaching practices. At each monthly staff meeting one teacher shares a classroom practice. Once per month our principal provides one hour of school time for “divisional meetings”. At this time all primary or all elementary teachers meet to share and discuss teaching practices. We often lead our own inservices to share our expertise in a particular area. Our principal encourages and provides time for a teacher to visit another teacher’s classroom to observe teaching practices.

Beyond our little school with so many opportunities for collaboration, our teachers are also encouraged and substitute time can be provided so that we can pursue professional development by visiting another school to collaborate with and observe a teacher at the same grade level.

Our classrooms are full of different students; different learning styles and we have a variety of material to cover. Teacher collaboration is critical to accommodate all that is presented in our classrooms and to effectively teach ALL our students. It is the best means of discovering alternate ways of teaching.    

Conceptualization and mathematical language

Conceptualization

This week in my Grade One class the focus in math has been on the concepts of 1more, 1 less, 2 more and 2 less. To differentiate instruction the students have worked on various activities to gain understanding of the concepts. In math class this week students used 10 Frames to show the concept, played two different games, completed a worksheet and a workbook page. Each day also involved some oral questioning on the topic. Through my observations of my students engaged in these activities I was certain that all but one student understood the concepts.

 Yesterday afternoon as a culminating activity I had all students make a “lift and seek book”. Their one page book, folded into three sections, read like this

                    Is 2 less than                           

(text varied-1 less than, 1 more than or 2 more than).  

Students had to choose a number and draw the corresponding dots on the first section, the phrase was in the second section and then of course students had to fill in the correct number and dots on the third page. Only four students completed their booklets correctly!

Mrs. Ryan learned that along with varying the instruction this week I should have been varying the mathematical language. All week throughout the various activities the language was consistently “what is 2 more than 7, show on your ten frame a number that is 1 less than 9, if you shake a 2 on the die then you put on two more blocks, etc.” Yesterday the language was turned around :12 is 2 less than                 . My students demonstrated lack of conceptualization of the concepts of more and less. An interesting lesson for me!

Differences

This week’s Ch. 9 of our text Experiencing School Mathematics has prompted much discussion around the topic of gender and the learning of math. Boaler’s study reveals that girls and boys have different learning styles when it comes to math. Because of the variation in learning styles girls or boys may be disadvantaged if only one form of instruction is instituted by teachers.

After reading many of our classmates postings on the issue of gender and mathematics and reflecting on my them, here are my thoughts:

It is my job to engage ALL of my students in learning activities that result in their gaining of knowledge. My job is not to “cover” curriculum outcomes, but to ensure that EVERY STUDENT in my class demonstrates learning of these outcomes. My job is to accept and teach my students as they are; different genders, races, abilities, family situations, socio-economic status, languages, exceptionalities and experiences.

I do not think that we need to spend our efforts in looking for the differences in our learners, or debating if they exist. Our efforts need to be invested in exploring methods to teach ALL our learners. By differentiating instruction we are giving all learners a chance to gain knowledge. If a student does not learn, then it is our job to try another teaching method.

Self-motivation and confidence

In chapter 8 of Experiencing School Mathematics by J. Boaler the terms self-motivated and confident are used to refer to the students of Phoenix Park School where math was taught using a reform approach where students engaged in inquiry based learning activities. These words struck me as I feel they reflect what we as teachers hope that all of our students achieve. When teaching we need to select the method that will instill this in our learners.

Students will gain confidence in mathematics as they work through problems, try applying what they know, ask questions, make mistakes, find other’s mistakes and correct errors. Students will gain confidence by doing math and seeing that they can do it.

Students will be self-motivated as they gain confidence and as they make connections with math and their lives, as they realize that they do need to know this stuff!

One other point that I’d like to share on student learning of mathematics….Is it any different from learning to sing, play piano, paint or play basketball or hockey? In these situations learning happens while engaging in the activity!

Chapter 7-my opinion

In our course text Boaler suggests that students at Amber Hill were disadvantaged in their procedural learning of mathematics. A result of this form of learning is that students forget rules and procedures over time.

I do not view memorizing formulas and rules as learning. To learn we must experience and connect. If students at Amber Hill are practicing procedures for a test and then forgetting the material there is no learning, no new knowledge has been acquired.
Is there really need to debate procedural learning over conceptual learning?

Thoughts on Math Assessment Practices/Ch.6

 In Chapter 6 of our course text Experiencing School Mathematics we are finding out how each of the two schools in the study of reform versus traditional teaching methods measure up. The researcher assessed the students through written tests and applied activities where written output from the students was graded.

I feel that more forms of assessment are necessary to fully view a student’s mathematical understanding. It is interesting that this chapter was the focus during the same time as discussions have come up in my school regarding the new assessment policy that has been implemented by the Eastern School District for NL.

Some points of interest from the document that contradict the assessment and teaching of the Amber Hill and Phoenix Park students are:
Teachers shall differentiate instruction and assessment, where appropriate, to support student learning.

 Assessment practices shall provide students with multiple opportunities to demonstrate learning in a variety of ways and contexts.

 A listing of recommended forms of assessment is also provided in the document as follows:

Teachers are expected to use a variety of data sources obtained in a variety of contexts to understand and determine student progress. These include, but are not limited to:

 a. Internal data sources:

Formal and informal observations with anecdotal records

Learning logs, journals

Performance-based assessments

o Projects

o Research Papers

o Student Presentations

o Labs

Self assessments

Peer assessments

Conferencing

Digital Evidence

Portfolios

Individual and group participation

Work samples

Reading records

Tests and examinations

b. External data sources:

Criterion-Reference Tests

Public Examinations

 Teachers are gaining clearer pictures of student ability by employing varying methods, students have many opportunities and means to show what they know.

In my Grade One class I do collect samples of student written work in math but I find that my best assessment comes from observing them carrying out math activities both independently and in groups. When my students are engaged in a math activity I travel around my classroom with a clipboard, jotting notes on students or marking off required outcomes on a checklist. Another valuable assessment practice I use in math is student interviews. I sit with my students individually and ask them to perform certain math tasks, answer math questions and solve problems. I started conducting these interviews with my students two years ago, at this time I had begun inserting marks on report cards based on my observations in class and my collection of written work. When I sat and interviewed I discovered that many of my students knew much more than I had given them credit for. This was an eye opener to the value of differentiated assessment.

 Reference

Administrative Regulations Policy IL – Assessment and Evaluation
(October 5, 2011) retrieved http://www.esdnl.ca/about/policies/esd/I_IL.pdffrom

Teaching Students Math Strategies

I have really struggled all week with thinking about the project based approach to math employed by the teachers of Phoenix Park. I don’t know if it is my primary teacher instinct, but I cannot get my head around teachers’ just assigning work and having students go at it with no direction, no deadlines and offering help only to those students that seem interested.

In my classroom (grade 1) I too present problems to my students, many times a day in fact. Anything I can turn into a math problem I seize the opportunity. When students attempt to solve problems I always have them share how they figured it out. I will ask students to share if they have figured it out in a different way. I think that students need to feel comfortable in being wrong, in taking time to think things through and in solving using different strategies. I also stress to my students the importance of not telling peers’ answers, but letting them have “think time” to try to solve independently.

Of course there are always students who never attempt to solve independently or contribute to math discussions. I feel it is my responsibility to work with these students to find out what they know. Lack of participation or lack of written output does not mean lack of knowledge or understanding. I work with these students, giving hints, providing manipulatives, or scaffolding the problem.

Finally, I do teach my students strategies to solve math problems. Whenever I present a problem I remind them of ways that they can help themselves to solve it. I want them to see that using strategies that work for them is the way we figure things out. I see that my little students need to develop a comfort with working out math in the way that suits them. Showing them strategies helps them with this. My young students will hide their hands under their desks if they need to count their fingers, I tell them that counting fingers is the right thing to do if that is what you need. When trying to name the next number in a sequence many students will look away from number charts because they think they should know, I tell them to use number charts if that is what works.

I use a balance of traditional and reform based teaching of mathematics. I feel it provides for optimum learning.

Thoughts on readings for week ending Oct. 5 -Forward, Introduction, Ch.2

I am very interested in reading the text and learning of the findings of the study carried out of the two vastly different schools and the different approaches to teaching mathematics.
I teach grade one and feel that my students learn best by being engaged in math activities that connect to their experiences. I encourage learning by allowing them to figure things out for themselves, by praising their mistakes and seizing moments to create more math problems to solve. I see my students learn most through interactingh with each other, playing games and exploring.
Then I come home to my children, one in Grade 8 and one in Level 3. My Gr. 8 girl (if gender has any influence) is complaining that she has a math test on Friday that she feels she will fail as her teacher stands at the board all class and puts up examples for them to copy. My son (level 3) is currently at a math tutor. He is capable, but does not listen well in class and does not practice the necessary skills (my diagnosis of his lesss than acceptable math marks). He has not provided me with much information on his math classes, but at curriculum night last week, his math teacher showed us the 300 page Practice Exercise workbook that is recommended at a cost of $25 as the text book that is provided is not adequate. The teacher also provided us with some websites where students get additional math instruction and practice. Sometimes his tutor will show him how to solve something in math but tell him not to tell his teacher that he knows how to do it this way!
Sorry if I am ranting...but there seems to be too many incongruencies between math in primary grades and math in high school. Are we creating six year old confident problem solvers who by the age of 12 are taught that there is only one correct way to do things and that they must do it over and over just like everyone else in the class????

What is math and why do we teach it?

Lakoff and Nunez (2000) refer to a romantic view of mathematics where a mathematician is someone who “is more than a mere mortal-more intelligent, more rational, more probing, deeper, visionary” (p.340). This is contradictory to the ideas on creativity expressed by Robinson when he compares the abilities of professors with those of dancers. He stresses the recognition that all people have intelligence or a talent in some areas. Not being strong at math does not make a person any less intelligent than a mathematician. It is simply their talent, or the area in which they are intelligent. Each person has the capacity to be highly intelligent in something, but not necessarily the same thing. This is an important notion for educators and something that needs to be shared with learners. My own children will often say how smart a classmate is I always correct them and restate that the person is smart in math or biology or merely more capable at studying and listening.

Despite agreeing that math is not everyone’s strength I do feel that math needs to be taught to our students, but more efforts need to be made to help them make connections to their own lives and to see the relevancy of studying math. I love to share with my little Grade One students the book Math Curse by Jon Scieszka (1995) just as an example that math is all around us and necessary to explore. We all use money, follow patterns, count, measure, compare and so on. I do not think that people connect all of this to mathematics. Students need to see these connections so that the study of math has more purpose for them. All will not become mathematicians, but all will need to use math. Musicians, actors and dancers need to keep time, carpenters must measure, cashiers must count money, etc. Davis  (1995) states that there needs to be a change in a math teachers thinking and actions from working to explain math to working at affording students experiences to interpret (p.23).

References

Davis, B.  (1995). Why teach mathematics? Mathematics education and enactivist theory. For the Learning of Mathematics, 15(2), 2-8

Lakoff, G.  & Nunez, R ( 2000)  . Where mathematics comes from. Basic Books: USA.

Math autobiography

My first mathematical memories are of the counting rhymes “One, two, buckle my shoe….” and “Ten little, nine little, eight little Indians”. I do not know who taught these to me but I do remember chanting them as a young child of 4 or 5 years old.  I am glad to see that I was exposed to both counting forward and back at an early age.

What I remember most about primary school mathematics is doing many pages of written work which I did enjoy. Teachers did a few examples on the chalkboard each day and students did many examples of the same concept in their exercises copied from the math text book. All work not completed in class was assigned for homework. Correct answers were called out in class the next day and we corrected our own books. Story problems were present at the end of most text book pages. I recall disliking them. At the end of each chapter we had a test.

Elementary school was a repeat of more of the same. For the most part I did enjoy math and achieved high grades. I grasped new concepts easily and loved doing the written practice.  To study for tests I always redid many examples of calculations from the current unit of study.

In grade 8 I continued to do very well in math, but many of my classmates found it difficult. I am not sure if the concepts became more difficult or if the teacher was unable to explain them adequately. After the usual chalkboard demonstrations and assignment of seatwork I set about helping my peers understand  the day’s math lesson. (I think the teacher counted on me for this! As I recall it being a daily occurrence and I was somehow labeled as “the brain” in the class. )  I listened and practiced and already seemed to have a knack for teaching! When I relay my on an individual basis Grade 9 experience you will see I was not the “math brain”.

In Grade 9 I was automatically placed in what was then called Honors Math. I got 60% in the first test and was demoted immediately to the regular stream.  It was a little blow to my ego, but I continued to listen to math instruction in class and practice the necessary skills daily and nightly.  I also continued to help my peers on occasion and enjoyed the work. Thus I continued to do well in math, always achieving A’s.

Onto university where I had my career as a primary school teacher all planned, therefore I needed only one math course … it was maybe something like Teaching Math in Primary Grades. I recall making absolutely no connections with math or anything else during this course.   The instructor was a male in his 50’s who did not speak English clearly. I recall only being so grateful that I did not have to do the brutal math courses that my friends had to do in first year as they pursued studies in Engineering and Commerce. It always bothered me that students were so ill prepared for university’s introductory math courses.

As a Grade One teacher I love teaching mathematics. I can have a lot of fun with it and so easily incorporate it into everything I do. I spend a lot of time connecting math to their everyday lives. We count how many days we’ve been in school, who is tallest, who has the longest and shortest names and so much more. I enjoy doing hands on activities with my students, they learn so much from each other. I spend a lot of time trying to have them explain how they know things and encouraging them that it is okay to have strategies to find out what we do not know. I am trying to bring my little students beyond answering that they know something “because”.  I give my students lots of praise and call them “Great Mathematicians” when they solve problems
One of the most valuable mathematical experiences I have had as a teacher has been conducting individual math interviews with my students. I have used observation and paper pencil activities as forms of assessment in the past, but the clearest picture of what  a student really knows is best seen when you get to talk to them on an individual basis about math and how they do things and know things.

test

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