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					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

				
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