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References for Lesson Analysis Assignment. 1.Key to students understanding was farmiliarity with Mathematical words and their meanings. But traditional methods of looking up words and definitions dont work. Students don' understand what definitions mean until they have grappled with the concepts to which the words are applied.(p.83 reason for encouraging discourse.) Kenny, Joan M. et el "Literacy strategies in improving Math Instruction" 2.Giving students a preview of what they are about to learn or experience helps them activate prior knowledge. This strategy gives students the opportunity to connect what they already know to what they need to know. Questions should focus on what is central and most important. **// Marzano’s instructional strategies http://www.tltguide.ccsd.k12.co.us/instructional_tools/Strategies/Strategies.html//////**

3. Nelson Canada: Choose your grade...then go to online teacher resources (up to grade 8)...then start... http://www.nelson.com/nelson/school/elementary/mathK8/companion.html



 Professional Learning Plan Assignment.

FOCUS: Making connections between different representations (t-tables, graphs, equations) CBAM Profile: Stage 2 (Personal)

**Misconceptions in Patterning and Algebra**
For students who chose to represent the data through a graph
 * Problem solving requires students to take risks. Students may be very self conscious and not want to embarrass themselves (//Leading Math Success//, page 44). This may result in hesitating to participate in the lesson.
 * Students might not understand that there is a logical order in the continuation of the pattern since they don’t have a complete understanding of number sense and so might determine results that vary from the true pattern.
 * Students might have some challenges with basic addition so come up with an incorrect answer (although he/she understands the concept.
 * Although students are exposed to variables in elementary school, they often enter secondary school with a very limited understanding of how they can be used (i.e. different letters can represent the same number in some equations) and conventions (i.e. ab = a x b, but 72 does not equal 7 x 2) (Van de Walle, 411).
 * Although students are exposed to variables in elementary school, they often enter secondary school with a very limited understanding of how they can be used (i.e. different letters can represent the same number in some equations) and conventions (i.e. ab = a x b, but 72 does not equal 7 x 2) (Van de Walle, 411).
 * Students might confuse the process different representations of patterns (i.e. charting in a t-chart versus graphing.
 * Students might not make connections between strands in the curriculum (i.e. data management and patterning/algebra).
 * Students might not understand that symbolic representation and drawings help them in solving problems and understanding ideas (Van de Walle, pg 303 ).

Objectives and key findings (page 1) ·  Awareness raising and behaviour change. ·  Learning how to learn is just as important as the acquisition of knowledge and skills. ·  Joint planning and resource development, with mutual observation and learning from one another. ·  Allow people to learn how to be effective learners. ·  Four main components of training: developing knowledge through exploring theory; the demonstration or modeling of the skill; the practice of the skill; and peer coaching ·  All four components will be increasingly necessary as the desired outcome becomes more complex. ·  Specific attitudes and skills are required of teachers to become effective learners including persistence, understanding of the transfer of training and the need for theory, and the ability to use peers productively. ·  Peer coaching leads to collegiality and experimentation. ·  The primary activity of peer coaching is collaborative planning.
 * Student Achievement through Staff Development (summary of reading) **
 * Training Objectives. **
 * Key Findings: **

· Training should provide people with required stills and provide them with an opportunity to use the new knowledge in practice. · Training also should support people in becoming effective learners. This can be accomplished by identifying the desired training outcome and providing targeted professional development which support the learner in reaching the outcome. · Targeted outcomes can be categorized as: o Knowledge or Awareness (i.e. learning about new educational theories, curriculum developments…etc.) o Positive Attitude Changes (i.e. towards curriculum) o Skill Development (i.e. how to effective questioning techniques) o Transfer of Training and Executive Control · Targeted outcomes can be easier to achieve when they are similar to an educators existing programming and practice. · Newer targets tend to be more difficult to achieve · There are four main components to training. All four are required if “transfer to the classroom is the objective of the training” (pg, 2) o Knowledge: Exploring and understanding theories, including the supports for it  o  Modeling of a new skill: o Practice: A period where the educator can practice and consolidate new skills (usually 8 – 10 weeks) o Peer Coaching: Educators collaboratively working together to plan, develop, and implement effective lessons
 * The Outcomes of Professional Development (page 2): **
 * Components of Training (page 2/3): **


 * How do teachers learn to acquire new skills?**(pg 3)
 * **Persistence**: every educator knows the importance of practice for children. From their evidence base the authors conclude that persistence, even when initially uncomportable, was a characteristic of successful learners.
 * **Acknowledgement of the transfer problem**: Teachers need to understand that the transfer of training is a separate learning task from the acquisition of knowledge of skills.
 * **Teaching new behaviours to students:** students are discomforted by change, especially when they are succeeding in existing conditions. Teachers who directly teach both the cognitive and the social tasks required by specific innovations are more likely to achieve successful transfer.
 * **Understanding the importance of the underlying theory**: teachers who master the theory underlying new behaviours are more likely to achieve similar results to those obtained in research settings, with their own students.
 * **Proactive and productive use of peers**: teacher who used peer support for mutual problem solving, observations, collaborative teaching and planning were more successful in transferring new skills to their own practice.
 * **Flexibility:** teachers need to develop a spirit of enquiry, a willingness to experiment with their own behaviour and an openness to evidence that alternatives have something to offer.
 * How coaching contributed to the transfer of training**(pg 3-4)
 * practiced new strategies more often and with greater skill than uncoached ed ucators wth identilcal initial training
 * adapted the strategies more appropriately to thier own goals and contexts that did uncoache teachers who tended to practice observed or demonstrated lessons
 * retained and increased their skill over time - uncoached teachers did not
 * were more likely to explain the new codels of teacheing to their students, ensuring that students understood the purpose of their strategy and the behaviours expected of them
 * demonstrated a clearer understanding of the purposes and use of the new strategies. the frequent peer discussions about them, including lessons and materilas design, seemed to enable them to 'think' with the strategies in ways which uncoached teachers never showed

** Coaching in an Organisation-wide Context (page 4): ** · Setting norms that support the improvement of teaching leads to other forms of change as well. · Peer –coaching teams must: o Commit to implementing the change o A ssist and support each other o C ollect data on student effects (based on the identified target) ·  Primary activity of peer coaching study teams: Achieve shared organizational goals through collaborative planning and development of curriculum and instruction · Staff developers can… o Assist teachers/schools in redesigning workspaces (for ex. begin to help them find time!) o Set up peer coaching teams on the first day of training (the sooner the better) o Provide examples (for ex. offer a structure or scaffold for a sample activity) o Build in time for coaching teams to monitor their implementation and determine the effects on the students · Authors acknowledge that this kind of initiative is pricey and time-consuming, but conclude that the investment is worth it ·  The design of the training should be closely related to the intended outcomes · Improvement initiatives require participation/commitment from everyone (in the school) · Leaders should determine most effective ways of monitoring PD activities to evaluate impact on student achievements
 * Where do we go from here? (page 4-5): **
 * What have we Learned about the Role of Training in Supporting Teachers and Leaders in the Acquisition and use of new Knowledge and Skills? (page 5) **

Your system's professional development plan will be informed by your system's:**
 * Planning Article:**
 * Planning Getting Started
 * vision and goals for mathematics learning, teaching, and leadership
 * Knowledge and beliefs regarding the change process, teaching, learning, professional development, and the nature of mathematics.
 * context within which you will implement strategies
 * analyses of data related to students' thinking, understanding, and achievement
 * purposes for each professional learning activity


 * Steps in desgning an effective long-term plan for professional learning:**
 * vision and goals
 * what outcomes will you strive for
 * What will you accept as evidence that you are reaching your goals
 * Asses where you are now
 * what do you know about the knowledge, beliefs, and needs of the stakeholders in your system


 * key Features of Powerful Mathematics Professional Development**
 * To improve student engagement requires:
 * classroom activity must center on mathematical understanding, invention, and sensemaking by all students.
 * the classroom culture msut support inquiry, wrong answers, personal challenge, collaboration, and disequilibrium as opportunities for new learning by all students.
 * the tasks in which students engage must be mathematically worthwhile for all students.


 * Six Key Professional Learning Clusters: **
 * In order to develop a ‘successful comprehensive mathematics professional development plan’ there are six ‘clusters of evidence’ that must be considered and embedded within the program.
 * 1) **Knowing Mathematics for Teaching** (i.e. content understanding).
 * 2) **Cultivating Mathematical Thought** (i.e. understanding and incorporating instructional practices which support students in the development of a deep understanding of mathematics).
 * 3) **Assessing Mathematical Understanding** (i.e. development of tools and strategies to effectively understand a student’s mathematical thinking).
 * 4) **Achieving the Potential of Standards-Based Mathematics Curricula** (the development and implementation of a high quality curriculum which is standards based).
 * 5) **Transferring Mathematics Leadership** (collaboration of teachers within a professional mathematics community where leadership is shared).
 * 6) **Extending Mathematics Learning** (closing the gaps in achievement through supplementing mathematics instruction with learning opportunities outside the classroom).

1. **Task Clusters** (page 90 of Literacy Strategies for Improving Mathematics Instruction Kenny Joan M. et el (2005) Elementary and Secondary Teachers in our Schools can bring in problems related to patterning and Algebra. Each cluster should include related problem from each grade and the following set of focus questions is provided for participants to disccuss:  ·  What is the core Mathematics that these tasks have in common?  ·  What additional mathematics concepts, skills are involved?  ·  Are there concepts and skills unique to certain tasks?  ·  For what grade level does each task seem appropriate?  Discussing these questions provide aunique opportunity see what underlying Mathematics is inhererent in all the problems . 2. **Summer Math for Teachers** (We can call this something else and not necessarily restrict it to summer) (Loucks-Horsley,Susan et el: Designing PD for teachers of Science and Mathematics. Page 52) Teacher’s teach other teachers Mathematical content while modeling new and different instructional strategies. “The program is based on the belief that teachers must become Mathematics learners if they are going to teach for understanding, that this happens best when they are challenged at their own level of Mathematical competence, and they must be provided with experiences as students in classrooms that are based on the same pedagogical principles as the ones they are expected to implement with their children”  3. **Lesson Study Community**: Using a collaborative approach, teachers identify a goal for student learning. The team develops a lesson which addresses the goal. While the lesson is being presented student learning, engagement and behaviour is monitored by team members. Following the lesson, the team works together to identify strengths and areas for improvement of the lesson and makes appropriate changes regarding instructional approach to the lesson plan. (Ideas for a Establishing Lesson-Study Communities).
 * PD MODELS THAT WE CAN LOOK AT: **

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