Document Sample

Literacy in Mathematics Literacy in Mathematics Within Curriculum for Excellence, literacy is defined as: the set of skills which allows an individual to engage fully in society and in learning, through the different forms of language, and the range of texts, which society values and finds useful. [Literacy across learning – Principles and practice] The three organisers within the literacy framework are: listening and talking reading writing In addition to these, in this document, we will include mathematical vocabulary. Literacy skills need to be taught systematically and consistently. Learners should be given regular opportunities to consolidate their literacy skills by using them purposefully in order to learn. All teachers have responsibility for promoting language and literacy development. Every teacher in each area of the curriculum needs to find opportunities to encourage young people to explain their thinking, debate their ideas and read and write at a level which will help them to develop their language skills further. [Building the Curriculum 1] Some subjects have clearer opportunities to develop aspects of literacy skills than others. Key literacy skills that can be developed in Maths include: Using talk to explain and present ideas Active listening to understand Reading for information Writing short and extended responses Where opportunities for listening, talking, reading and writing should permeate a learners experience in mathematics there are maths and numeracy outcomes where these skills are explicitly stated. For example: „Having explored …..‟ „I have worked with others …..‟ „Having investigated …..‟ „I have discussed …..‟ „Sharing my solutions/approaches with others …..‟ „..… using mathematical language …..‟ „Explaining my choice of method‟ „….. using appropriate vocabulary …..‟ „Having investigated different routs to a solution ….. „I can describe …..‟ „I have explored with others …..‟ „When analysing information …..‟ 1 Listening and Talking Effective listening and talking is most effective when teachers plan activities in their lessons that promote and develop these skills. Listening and talking can enhance the learning of mathematics when: learners have regular opportunities to explain and justify their understanding of mathematical concepts learners are given opportunities to discuss and explore ideas with each other, and share their mathematical reasoning and understanding learners work collaboratively learners use correct mathematical vocabulary Mathematical discussion is an activity in its own right, as well as an integral part of other tasks. Focusing on strategies and explanation more than simply eliciting answers will provide many opportunities for one- to-one, group and whole class discussion during maths lessons. Examples of opportunities for discussion: exploring mathematical concepts describing visualisations of shapes, movements and constructions explaining calculation strategies and talking about methods for the solution of problems reasoning in working towards a solution and justifying results comparing different mathematical processes for their efficiency and effectiveness talking about mathematical expressions using mathematical and non-mathematical language discussing which mathematical equipment and materials to use comparing different solutions in order to arrive at a correct solution discussing and interpreting data and drawing conclusions presenting their findings to an audience For effective group discussion to take place: the purpose and outcome of the task must be explicit group discussion is managed effectively, e.g. taking turns, listening to others all learners are engaged, e.g. by assigning roles clear time limits are set Approaches such as Dialogic Teaching, Cooperative Learning and Critical Skills offer effective strategies for teachers to provide structured opportunities for pupil dialogue in the classroom (see Appendix 1). Links to Literacy Outcomes Learners have many opportunities to engage in discussion of appropriate complexity and they know how to engage in pair and group discussion. 3-02a, 4-02a, 3-10a, 4-10a 2 Useful Resources The Improving Learning in Mathematics resource builds on existing successful practice and explores approaches that encourage a more active way of learning through the use of group work, discussion and open questioning. The full resource can be downloaded or viewed online here: http://teachingandlearning.qia.org.uk/teachingandlearning/downloads/default.aspx#math_learning For suggestions on managing group discussion refer to the Challenges & Strategies document pp30-41. http://tlp.excellencegateway.org.uk/pdf/Improving_learning_in_maths.pdf Bowland Maths professional development Modules are excellent resources for personal or departmental use. Module 3: “Fostering and managing collaborative work‟ – How can I get them to stop talking and start discussing?” looks at the characteristics of effective pupil-pupil discussion and the teacher‟s role. http://www.bowland.org.uk/ – click the Professional Development link „Questions & Prompts for Mathematical Thinking‟ and „Thinkers: A Collection of Activities to Promote Mathematical Thinking‟ from the Association of Teachers of Mathematics ( http://www.atm.org.uk/) provides a wide range of mathematical questions and prompts to stimulate discussion, enquiry and critical thinking. Maths4Real videos used with the accompanying worksheets encourage learners to listen and extract relevant information during the course of the video. The „Tick or Trash‟ activity provides an opportunity for discussion of solutions, common errors and misconceptions. The Maths4Real videos and supporting resources can be viewed or downloaded freely from the TeachersTV website (http://www.teachers.tv/maths4real) Classic Mistakes www.classicmistake.co.uk a collection of common errors and misconceptions to promote discussion. A „Clue Cards‟ activity can be effective in developing listening skills along with problem solving and information processing. Some examples can be found at http://numeracy.cumbriagridforlearning.org.uk/getfile.php?src=684/group_problem_solving.pdf 3 Reading Reading in mathematics involves a range of skills, including visualisation, interpretation, recognising terminology, numbers, and symbols, recognising patterns and relationships in mathematics, following instructions and reading and understanding mathematical questions and problems. Reading skills underpin information processing skills. These enable learners to find and organise relevant information, to compare and contrast it and to identify and analyse relationships when using and applying mathematics. Explicitly teaching reading skills to do this helps learners to process information more effectively. In Maths, learners need to read text from a variety of sources, including: Instructions Questions Explanations Tables Diagrams Graphs and Charts Expressions and equations Data These situations happen naturally throughout maths lessons, but the learners ability to process information from these different sources is possibly taken for granted. Teachers need to use a range of strategies and activities to help develop learners‟ reading skills. Reading in mathematics is further complicated as learners an often expected to read „backwards and forwards‟ to find information and are frequently required to interrupt their reading to carry out calculations Links to Literacy Outcomes Learners can identify main concepts from different texts, make inferences using supporting detail and identify similarities and differences between different types of text. 3-04a, 4-04a, 3-07a, 4-07a, 3-14a, 4-14a Learners use strategies before and when they are reading to monitor and check understanding. 3-12a, 4-12a, 3-13a, 4-13a 4 Some strategies which can enable learners to engage with texts in active ways, i.e. by having something specific to do with the text, include: highlighting o e.g. highlight or underline specific information such as key words or phrases supplying missing words or phrases o e.g. in text, expressions, tables, diagrams, charts, labels, etc sequencing o e.g. getting learners to correctly sequence the steps in a solution matching o e.g. matching cards showing multiple representations of the same mathematical concept classifying o e.g. odd-one-out, Carroll diagrams evaluating mathematical statements o e.g. true/false, always/sometimes/never summarising o e.g. condense facts/processes into key points o produce synopsis from researched information Using such strategies as group or paired activities ensures that oral work is incorporated. The activities are designed to be interactive as well as active. There are examples of some of the above strategies in Appendix 2. 5 Writing In mathematics, the use of words may be replaced by writing algebraic expressions and drawing tables, graphs, diagrams and charts. Learners need to be taught how to use correct algebraic conventions and to label diagrams correctly, so that the meaning is correctly conveyed without ambiguity. Many learners find writing in mathematics difficult. Developing learners‟ ability to produce short written explanations will also encourage improvement in longer written tasks. The development of written mathematical language does not happen spontaneously, it needs to be taught. Examples of teaching strategies which help learners to improve their skills in writing in mathematics lessons are modelling, including the use of sentence starters and connectives. Modelling involves the teacher demonstrating how to do something whilst explicitly thinking through the process and decisions that are normally hidden. As teacher‟s model, they can also demonstrate the need to make alterations and corrections, revise and edit information, such as: how to begin how to select information which is relevant to the task or audience how to organise the information or ideas the use of protocols relating to the presentation of information or ideas how to end Modelling helps learners to develop the confidence to use these processes themselves. Encouraging the use of sentence starters and connectives can improve the clarity of explanations. Some examples are given below. An extended list is given in Appendix 3. Sentence starters: I noticed that…, I began by… Connectives: and, also, as well as, then, next, similarly, therefore, however, for example Encouraging learners to reword questions is a simple strategy that can be used to help develop more extended answers. Discourage the option for yes/no answers. 6 Links to Literacy Outcomes Learners have opportunities to create texts to communicate information, explain processes, summarise findings and draw conclusions. 3-06a, 4-06a, 3-09a, 4-09a, 3-26a, 4-26a, 3-28a, 4-28a, 3-29a, 4-29a Learners use a range of strategies and resources to spell most of the words they need to use, including specialist vocabulary, and they ensure that their spelling is accurate. 3-21a, 4-21a Learners are encouraged to punctuate and structure sentences and paragraphs appropriately. 3-22a, 4-22a Learners are given the opportunity to review and edit their work to ensure it meets its purpose and communicates meaning at first reading. 3-23a, 4-23a, 3-26a, 4-26a Learners consider the impact of layout and presentation as appropriate to audience. 3-06a, 4-06a, 3-24a, 4-24a 7 Mathematical vocabulary Learners should be taught the technical and specialist vocabulary of subjects and how to use and spell these words. Teachers often use informal, everyday language alongside technical mathematical language. Although this can help learners to grasp the meaning of different words and phrases, a structured approach to the teaching and learning of vocabulary is needed if learners are to use correct mathematical terminology themselves. Subject-specific terminology is important, because it enables teachers and learners to convey precise meaning. However, not all words in mathematics are unambiguous; many words used in mathematics are also used in everyday contexts, where they have a different meaning, e.g. bracket, origin, volume. Words used in mathematics often have a precise definition but are used more loosely in everyday contexts, e.g. diagonal, similar. Strategies to promote mathematical vocabulary include: be a role model – use correct mathematical language and notation and expect learners follow suit encourage learners to expand on their answers rather than give single-word responses highlight new vocabulary at the time it is in use in the topic, so that learners see how it is used in context display mathematical vocabulary around the classroom create word banks, topic displays, posters ensure that, as well as introducing new vocabulary, learners consolidate familiar terms be explicit about specialist vocabulary and ensure that learners have opportunities to pronounce, explore and practise using new vocabulary use every opportunity to draw attention to new words or symbols with the whole class, in a group or when talking to individuals provide abundant opportunities for pupils to engage in mathematical dialogue Links to Literacy Outcomes Learners use a range of strategies and resources to spell most of the words they need to use, including specialist vocabulary, and they ensure that their spelling is accurate. 3-21a, 4-21a 8 Appendix 1 Dialogic Teaching "Dialogic Teaching" means using talk most effectively for carrying out teaching and learning. Dialogic teaching involves ongoing talk between teacher and students, not just teacher-presentation. Through dialogue, teachers can elicit students' everyday, 'common sense' perspectives, engage with their developing ideas and help them overcome misunderstandings. When students are given opportunities to contribute to classroom dialogue in extended and varied ways, they can explore the limits of their own understanding. At the same time they practice new ways of using language as a tool for constructing knowledge. By engaging students in dialogue, teachers can: explain ideas clarify the point and purpose of activities 'model' scientific ways of using language help students grasp new, scientific ways of describing phenomena [University of Cambridge Faculty of Education – http://www.educ.cam.ac.uk/research/projects/dialogic/whatis.html] Some simple tips for developing a dialogic teaching approach: DO DON’T Choose questions and topics which are likely to Merely ask pupils to guess what you are thinking challenge pupils cognitively or to recall simple and predictable facts Expect pupils to provide extended answers which Tolerate limited, short answers which are of little will interest others in the class interest to other pupils Give pupils time to formulate their ideas and Hope for high quality answers without offering views through use of response partners preparation or thinking time Provide models of the patterns of language and Expect pupils to formulate well thought out the subject vocabulary to be used responses without the language to do so Routinely repeat or reformulate what pupils have Expect pupils to speak for all to hear said Vary your responses to what pupils say: debate with pupils; tell them things in order to extend the Just ask questions dialogue Signal whether you want pupils to offer to answer Habitually use the competitive, hands up model of (hands up) or to prepare an answer in case you question and a answer work invite them to speak Value talk as a tool for thinking and learning Don‟t talk when pupils could be talking Do expect pupils to listen with respect and respond appropriately [Dudley Grid for Learning] 9 Cooperative Learning Cooperative learning is an approach to organising classroom activities into academic and social learning experiences. Students must work in groups to complete the two sets of tasks collectively. Everyone succeeds when the group succeeds. [Wikipedia definition – http://en.wikipedia.org/wiki/Cooperative_learning] Useful links: Highland Cooperative Learning Academy website – www.highlandcla.wikispaces.com Cooperative learning structures, lesson plans – http://highlandcla.wikispaces.com/Lesson+Plans , The Cooperative Learning Network – http://lcandler.site.aplus.net/indexcl.htm Some examples of cooperative learning structures are given on the next page. Many more structures exist and under a variety of names. Further examples can be found at www.utexas.edu/academic/diia/research/projects/hewlett/cooperative.php Critical Skills The Critical Skills Programme, originally developed in the USA, is a well developed and structured system of learning and teaching which is transforming many schools and classrooms across the UK. [Learning & Teaching Scotland – www.ltscotland.org.uk/5to14/specialfocus/scots/ideas/criticalskills.asp] More information is available at the Critical Skills website – www.criticalskills.co.uk 10 Think, Pair, Share How it is done: A problem is posed; learners think alone about the question for a specified amount of time. During this thinking time the learner could make notes, highlight, organise, etc. Thinking time could be between lessons, i.e. a homework task. Following the thinking time period pairs are formed, structured by teacher. During the pair stage only one person should be talking while the other listens then switch roles. The teacher might give the listener something in particular to listen for, e.g. key word/phrase, skill, etc. During the share time, learners are called upon to share with the class as a whole. Where it can be used: When revisiting a topic, from a previous year, term, or lesson. For example, brainstorm what you can remember about Pythagoras, calculations involving percentages, etc. Top Tip: Use a timer to countdown time remaining. This focuses learners and helps keep them on task. It can also improve the pace of your lesson. Rally Robin How it is done: This involves learners taking turns in partnerships sharing information. Pupil one says a word or and idea, then pupil two, then back to one again, and so on... Where it can be used: It is ideal for getting learners thinking about a topic that they might have not covered for a while, or to start a lesson by recapping what they remember about the previous lesson and for brainstorming vocabulary. Round Robin How it is done: Similar to Rally Robin, but involves learners taking turns in a team, sharing information in oral form. Rally Coach How it is done: Partners take turns, one solving a problem while the other coaches. One pupil can have question cards together with the answers on the reverse. The 'coach' asks their partner the question and initially also tells them the answers. The second time around the coach does not tell them the answers, but gives them 'clues' if they need them. Top Tip: Have a mixture of questions that recap previous lessons and some new information. 11 Appendix 2 Classifying Odd One Out Carroll Diagram Numbers that are Numbers that are not multiples of 9 multiples of 9 Numbers that are multiples of 6 Numbers that are not multiples of 6 12 Evaluating Which one of these statements is true? 1 A. 0.33 is bigger than 3 1 B. 0.33 is smaller than 3 1 C. 0.33 is equal to 3 D. You need more information to be sure [Mathematics inside the black box – Hodgen & Wiliam] Always, Sometimes, Never Consider each statement in turn and decide whether the statement is always true, sometimes true or never true. All members of the group must explain their thinking and all members of the group must agree the decision. Doubling a number When an odd number is makes it bigger. squared the product is odd. A regular polygon has the Multiples of 5 are also same number of lines of multiples of 10. symmetry as sides. The larger the perimeter, To multiply by 10 you the larger the area. add a zero to the end. A quarter turn clockwise is Subtracting numbers the same as 3 quarter turns makes them smaller. anticlockwise. An even number that is a A polygon has 4 sides. multiple of 3 is also a multiple of 6. 13 Sequencing The following cards include three cubic functions and all the steps required to find their stationary points and to determine the nature of those stationary points. Learners have to sort the cards/steps into an appropriate order for each of the three functions. [Improving Learning in Mathematics – Calculus 5] 14 Matching 15 Appendix 3 The following examples of sentence starters and connectives could be displayed in the classroom. Learners could be encouraged to use these when giving oral and written responses. Sentence starters: I noticed that….. I tested… I decided to……so/that/because….. I tried….. I wondered why…. I noticed a connection between…. When I looked….. This didn‟t work so…. I already know that…so… This is true because…. Using the numbers in my table…. This reminded me of…. This worked so…….. Connectives: For adding information – and, also, too, as well as For sequencing ideas or events – then, next, afterwards, since, firstly, secondly, finally, eventually To compare – like, equally, similarly To contrast – but, instead of, alternatively, otherwise, unlike To show cause and effect – because, so, therefore, thus, consequently To further explain an idea – although, however, unless, except, apart from, yet, if, as long as To emphasise – in particular, especially, significantly To give examples – for example, such as 16

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 3 |

posted: | 1/16/2012 |

language: | |

pages: | 17 |

OTHER DOCS BY keralaguest

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.