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