Family_A

=WE ARE FAMILY A(wesome) =

Members:
===Mariam, Maxwell, Naheed, Stephanie   ===

Summary of Analysis:

 * There were some difficulties across the continuum regarding number sense e.g. order of operations, algebraic manipulation, understanding of exponent rules.
 * The scores for questions that required straightforward application of knowledge were good.
 * Scores were particularly low for problems requiring application of algebraic concepts to a various situations. However, similar trends were evident at the board and ministry level.

Our Question:
====**How can we improve the strategic competence of at-risk students in problem solving involving patterning and algebra through the use of various representations (diagram, tables, graphs, etc.) in real-life situations?** ==== 



Target:
<span style="color: rgb(250, 90, 0)">

=
<span style="color: rgb(0, 0, 0)"><span style="color: rgb(254, 142, 22)"><span style="color: rgb(246, 104, 44)"><span style="color: rgb(255, 0, 0)"><span style="color: rgb(0, 0, 0)"><span style="color: rgb(255, 0, 0)"><span style="color: rgb(0, 0, 0)"><span style="color: rgb(250, 90, 0)">**Students will demonstrate strategic competence with patterning and algebra in solving real world problems.**       =====

==<span style="font-size: 120%; font-family: Arial,Helvetica,sans-serif; text-align: center; display: block"><span style="font-size: 120%; font-family: Arial,Helvetica,sans-serif; text-align: center; display: block">Resources for Lesson Analysis ==

** Teaching and Learning Mathematics (Junior Grades) **

 * During the junior grades, mathematical understanding is broadened as students begin to make connections between concepts learned and are encouraged to apply concepts learned in new situations. This extends to approaching a problem in multiple ways. (1)
 * Communication skills are further developed as students in the Junior grades begin communicating their thoughts in multiple ways (i.e. orally, on paper…etc.). This extends to communicating their ideas in an organized fashion which could be understood by peers and the teacher. (15).
 * An understanding of the structure within mathematics is fostered through discussions, explanations, and examinations of how one question can be approached from multiple perspectives (15).
 * <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> Appropriately math games and puzzles provide an opportunity for students to refine their proficiency in content understanding (23).
 * <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> Use of manipulatives provide several benefits including supporting students in the processes of visualizing the concept (25) As a side note, there was a study released in April saying that manupulatives do not benefit learning as much as we’ve been led to believe (just an interesting fact, if we talk about manipulatives we might want to include, I have an article about it at home)
 * <span style="font-family: 'Times New Roman',Times,serif"> <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> Students whom do not have a solid understanding of fundamental mathematical concepts benefit when the mathematical problems presented by the teacher contain a variety of entry points, and are broad enough so that they can be solved through a number of different strategies (37).
 * <span style="font-family: 'Times New Roman',Times,serif"> <span style="font-family: 'Times New Roman'; font-style: normal; font-variant: normal; font-weight: normal; font-size: 7pt; line-height: normal; font-size-adjust: none; font-stretch: normal"> “Effective assessment and evaluation practices have the capacity to greatly strengthen a student’s mathematical literacy” (quote, 41). Assessment is a tool which is used to support the learning of each individual student (41).


 * Early Math Strategy**
 * Focus on important mathematical concepts or “BIG IDEAS” (pg. 15)
 * Teaching through problem solving (pg. 16)
 * Use resources that aid understanding(pg. 19)
 * Concrete materials(Manipulatives) (pg 19)
 * Computer software (pg. 27)


 * Leading Math Success - Mathematical Literacy (grades 7 to 12)**
 * Connectionist teaching : "Value students' methods, use students' understanding and place emphasis on making connections within Mathematics"(p.29).
 * Introduce most skills and concepts through problem solving. (p.47)
 * Encourage persistence in meeting challenging goals. Give hints not answers. (mine)


 * Education for All (all grades)**
 * "Action Plans" that highlight efficient and effective ways to perform complex tasks. (p. 65)
 * Assessment strategy: Use various types of assessments to allow students to better demonstrate their understandings (performance tasks, etc.) (p. 75)
 * Math problem-solving instruction should be overt, systematic and clear, and scaffolded by the teacher and peers. (p.77)
 * Encourage the use of highlighters/underlining to extract important information. (mine)

**Potential Resources:**

 * Teaching and Learning Mathematics: The Report of the Expert Panel on Mathematics in Grades 4 to 6 in Ontario
 * Elementary and Middle School Mathematics (Canadian Edition), John Van De Walle & Sandra Folk
 * About Teaching Mathematics, A K-8 Resource, Marilyn Burns
 * Teaching Student-Centered Mathematics (Grades 3-5), John Van De Walle & LouAnne Lovin
 * The Ontario Curriculum, Grades 1-8 Mathematics
 * Early Math Strategy pages 20 to 24 provides a list of manipulatives and their connection to mathematical concepts and skills
 * Education for All: The Report of the Expert Panel for Literacy and Numeracy Instruction for Students With Special Education Needs, Kindergarten to Grade 6
 * TIPS4RM: Mathematical Processes
 * [|Resource list for Differentiated Instruction]

http://www.montgomeryschoolsmd.org/departments/itv/MathDude/MD_Algebra1_1-3.shtm
 * Math Dude (video clips introducing concepts)

This paper explores the development of students’ knowledge of mathematical procedures. Students’ tendency to develop rote knowledge of procedures has been widely commented on. An alternative, more flexible endpoint for the development of procedural knowledge is explored here, where students choose to deviate from established solving patterns on particular problems for greater efficiency. Students with no prior knowledge of formal linear equation solving techniques were taught the basic transformations of this domain. After instruction, students engaged in problem-solving sessions in two conditions. Treatment students completed the “alternative ordering task,” where they were asked to re-solve a previously completed problem but using a different ordering of transformations. Those completing alternative ordering tasks demonstrated greater flexibility. [|http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WD1-4H5MYFW-1&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=4de88000ec1d2fec642779cae713a6b8<span] style="display: block; text-align: right"> ||
 * **ScienceDirect**
 * ** Abstract **

= Does Comparing Solution Methods Facilitate Conceptual and Procedural Knowledge? = Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventh-grade students to learn about algebra equation solving by either (a) comparing and contrasting alternative solution methods or (b) reflecting on the same solution methods one at a time. At posttest, students in the compare group had made greater gains in procedural knowledge and flexibility and comparable gains in conceptual knowledge. These findings suggest potential mechanisms behind the benefits of comparing contrasting solutions and ways to support effective comparison in the classroom. Link is broken. ||
 * Journal:
 * **Abstract:**

Hey Group,

Here is an atempt at my rubric, I left the thinking category out since I don't really like the ones I have. Any ideas? I was thinking we could all edit on the page and then we'll all have the same one...I know the first two categories for K&U are specific to Grade 6, but I think the other sections are transferrable.

** Patterning and Algebra Rubric for Rich Task ** (Thinking) ||  Shows limited effectiveness. || Shows some effectiveness. || Shows considerable effectiveness. || Shows a high degree of effectiveness. || (Communication)  ||  Shows limited effectiveness. || Shows some effectiveness. || Shows considerable effectiveness. || Shows a high degree of effectiveness. || (Application) || Shows limited effectiveness. || Shows some effectiveness. || Shows considerable effectiveness. || Shows a high degree of effectiveness. ||
 * ** Categories ** || ** Level One ** || ** Level Two ** || ** Level Three ** || ** Level Four ** ||
 * Describes and represent relationships in growing patterns (Knowledge and Understanding) ||  Demonstrates a limited understanding  ||  Demonstrates some understanding  ||  Demonstrates considerable understanding  ||  Demonstrates a thorough understanding  ||
 * Determines the term number of a given term of a growing pattern (Knowledge and Understanding) ||  Demonstrates a limited understanding  ||  Demonstrates some understanding  ||  Demonstrates considerable understanding  ||  Demonstrates a thorough understanding  ||
 * Organization of ideas and expression of mathematical thinking using mathematical vocabulary
 * Making connections within and between various mathematical ideas