7.+Implications+for+Classroom+Teachers

= Superior Greenstone District School Board = = Student Work Study Initiative = = Learning Supposition for 2012-2013 =

Written by Kathleen Schram
= Implications for Classroom Teachers = In Kathy Richardson’s series of Assessing Math Concepts (2003) she notes that children’s early experiences build the foundation for the work in the later years. “If children are to be successful in the study of mathematics throughout their schooling, it is vital that the mathematics they learn be meaningful to them” (pg. 3). Too many students see math as a process of memorizing rules and procedures. We must help develop this understanding in our primary students. Often number sense does not get developed deeply in the primary grades and then the focus of teaching becomes that of facts and skills. Rather than repeating a process the child does not understand, it is important to determine what mathematics the child knows and what the child still needs to learn. “There are many children who are successful in completing math assignments but who are not learning the essential mathematics necessary for future success in their study of mathematics” (Kathy Richardson, __Assessing Math Concepts,__ pg. 3). Teachers need to increase their content knowledge around foundational ideas to be able to understand what mathematics the children are (or are not) learning. “They must recognize that what is required of children when they are asked to solve problems using procedures (whether they understand them or not) is different from what is required of children who are asked to demonstrate an understanding of the underlying mathematics.”
 * == Developing Early Number Sense ==
 * == Building Content Knowledge ==

Liping Ma (Knowing and Teaching Elementary Mathematics, 2010) refers to how Shulman (1986) describes pedagogical content knowledge as “the ways of representing and formulating the subject to make it comprehensible to others.” //**Are you able to make multiple representations to help meet the needs of your learners?**// The Third Teacher monograph speaks to the importance of designing the learning environment. Take the time necessary at the beginning of the year to establish those conditions that are necessary for learning to take place in your classroom. Help your students see themselves as mathematicians.
 * == Establishing the Learning Environment ==

In Math Exchanges (2011) Kassia Omohundro Wedekind states that "in order to achieve a deep and true understanding of mathematics, children must first see themselves as becoming mathematicians. They must identify themselves as mathematicians, take on the responsibility of learning to do the work of a mathematician, and make meaning of their world through mathematics" (pg. 11). She speaks about the importance of developing identity-building statements such as: "In order to build a community of mathematicians, we must spend time constructing the identity and work of individual mathematicians and a mathematical community as a whole; this work necessitates a combination of both planned and spontaneous moments" (pg. 14-15). Whether it be through small group instruction, 'math exchanges' or individual conferencing/interviews with students, we need to be interacting more with the work our students are doing so that we can gain insight to their thoughts. Often "teachers can be misled into thinking that children are making the progress necessary to move on to more complex ideas when they get right answers without understanding the underlying mathematics......What young children know and understand can number be fully determined through paper and pencil tasks. Teachers can get much more complete and useful information if they watch and interact with the children while they are doing mathematical tasks. (Kathy Richardson, Assessing Math Concepts pg. 11)
 * Mathematicians are curious.
 * Mathematicians ask themselves questions.
 * Mathematicians need lots of time to thin, think, think.
 * Mathematicians look for challenging problems in their world to figure out.
 * Mathematicians persevere.
 * Mathematicians make lots of mistakes, but they keep on thinking.
 * Mathematicians change their ideas and strategies and come up with new ones. Then they change their ideas again. This is part of being a mathematician.
 * Mathematicians talk to and question other mathematicians in order to help themselves understand.
 * Mathematicians do not always agree! Disagreeing respectfully is a part of being a mathematician.
 * Mathematicians work together. They explain their ideas and thinking. They listen to the thinking of other mathematicians
 * == Interacting More with Students as they are Working ==

We need to be more responsive in our planning - basing it on student need, planning with a purpose and reflecting on the progress we are making.



Kassia Omohundro Wedekind imagines the cycle of math exchanges as presented in Figure 3.1 (left)....that these types of interactions with students offer teachers a view of what children are able to do and allow for planning on where they should be going next. "In my experience, it is this kind of ongoing, day-to-day assessment that proves the most useful for guiding our work in math exchanges." (pg. 44)

When students understand the relationships between various mathematical models and how their thinking strategies can be represented in various ways; they can justify and demonstrate their thinking more clearly, making their thinking visible. It is important for teachers to explicitly model the use of various math tools (manipulatives, hundred chart, ten frames, reknreks, number lines and provide intentional opportunities for sharing of techniques/methods used between students. "When students create and share multiple representations of the same problem or situation, they are continuing to keep their thinking alive. Multiple representations also may provide deeper, more elaborate understandings of the underlying mathematics, and fresh, new insights into the problem.
 * == Modelling Multiple Representations and Explicitly Linking Relationships Between Them ==

Communication in the Mathematics Classroom monograph speaks to this around the importance of teachers recording mathematical annotations on and around student work: Skillful questioning can be very effective in enhancing the cognitive abilities of students and helps to get to underlying misconceptions and understandings. The process of effective questioning takes time to develop and includes establishing an appropriate environment, creating a climate conducive to learning, using an appropriate mix of questions, phrasing questions accurately, providing sufficient wait time, and using various probes in responses to the answers given by students.
 * == The Importance of Effective/Essential Questions ==

The Asking Effective Questions in Mathematics monograph provides great insight into what’s needed to be provoking student thinking and deepening conceptual understanding in the mathematics classroom

Jay McTighe & Grant Wiggins (2013) in their book Essential Questions state that, “In the first place, an educator’s job is not to simply //cover// content. Our role is to cause learning, not merely mention things. Our task is to //uncover// the important ideas and processes of the content so that students are able to make helpful connections and are equipped to transfer their learning in meaningful ways. If we perceive our role as fundamentally a deliverer of content, then talking fast in class is the optimal instructional method! But if we wish to engage learners in making meaning of the learning so that they come to understand it, then essential questions will serve the cause of mastery of content." (pg. 26)

In Small Steps, Big Changes, Confer and Ramirez note that: “Intentionality is more than taking the first step. Intentionality means making sure that the newly planted tree is in the right spot, in the proper soil, and that it gets the appropriate amount of water. In education, intentionality means persisting when the students don’t ‘get it’ the first time. Intentionality means not teaching the same thing ‘louder and longer,’ but looking for a different way to reach the children. Because ultimately, intentionality is believing with all your being that your students can be successful at math and that you will find a way to make that happen. (pg. 130)
 * == Being Intentional ==

“Although it’s true that the best time to plant a tree was twenty years ago..... and the best time to begin partner talk was when the students were in kindergarten.... and the best time to allow the students to solve a problem with different strategies was at the beginning of the year.... **....the second best time is now!”** (pg. 138) = = = Other Resources: = Just click on the image to link to more information