Multiplicative Thinking – PLC Resources

The Learning Assessment Framework for Multiplicative Thinking
http://www.education.vic.gov.au/Documents/school/teachers/teachingresources/discipline/maths/assessment/lafcomparativ.pdf

http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/learnassess.aspx

Scaffolding Numeracy in the Middle Years
http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/learnassess.aspx

Common Misunderstandings – Multiplicative Thinking
http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/learnassess.aspx

Newman’s Error Analysis – You will need to log in to PAT Teaching Resources (email as user name)
https://oars.acer.edu.au/norwood-primary-school Then go to Teacher Resources

Multiplication and Division – Maths Assessment Project
http://map.mathshell.org/download.php?fileid=1592

 

Our learning progression brainstorm (using Multiplicative Thinking article):

Content:

  • counting and splitting
  • skip counting
  • large collections
  • repeated addition (2s, 5s, etc.)
  • repeated subtraction
  • hold both numbers in head – number of objects within each group and number of groups
  • hold both numbers and the total
  • visualise 3×4, 4×3 move from additive to multiplicative strategies
  • factors, product – arrays
  • multiplication and division – commutative, inverse relations
  • language develops – for each, times, as many
  • symbolic representation, diagrams

Implications for teaching/ learning

Pedagogy:

  • Developing opportunities for students to use effective strategies – arrays
  • Challenge to show different ways
  • Communicate – in different ways
  • Explicit role modelling
  • Language used by students – allow opportunities for talk, and for listening in to hear their language (gaining insight into their thinking)
  • Variety of representations – words, pictures, symbols
  • Moving from familiar to unfamiliar contexts
  • Questioning and enabling prompts
  • Allow opportunities for collaboration
  • Think boards
  • Visualisation – drawing how they see the problem

 

 

SPELD Resources – Recommended for Dyslexia

SPELD – Cleve Bytes – Good Teaching Practices
http://www.speld-sa.org.au/services/clever-bytes-good-teaching-practices.html

SPELD Blog
https://speldsa.wordpress.com/

Assistive Technology
Kidspiration
http://www.inspiration.com/Kidspiration
https://www.speld-sa.org.au/shop/assistive-technology/product/217-wordq-4.html

For Mathematics

  • Directly teach the vocabulary of maths
  • Direct and explicit teaching
  • Focus on what the symbols mean
  • Teach step by step directions
  • Use concrete materials where possible initially and then more to abstract concepts
  • Use graph paper to help in organising ideas

 

Effective Instruction with Differentiation and Continuous Monitoring

Assistive Supports

Remediation

Accommodation

Modification

Strategic Intervention

Compensation

Assistive supports – specialised equipment, technologies, medical or physical devices, and other resources that help students

Remediation – strategies that teach students specific, usually prerequisite, skills to help them master broader curricular, scope and sequence, or benchmark objectives

Accommodations – change conditions that support student learning – such as the classroom setting or setup, how and where instruction is presented, the length of instruction, the length or time frame for assignments, or how students are expected to respond to questions or complete assignments.

Modifications – involve changes in curricular content – it’s scope, depth, breadth, or complexity

If target students don’t respond more significant or complex approaches from the next areas may be needed:

Strategic interventions – focus on changing students’ specific academic skills or strategies, their motivation, or their ability to comprehend, apply, analyse, synthesise, or evaluate academic content and material. Strategic interventions typically involve multidisciplinary assessments.

Compensatory Approaches– help students to compensate for disabilities that cannot be changed or overcome

 

A Closer Look at Spelling in the Primary Classroom – G Oakley, J Fellowes, PETAA

Notes:

Spelling is not learned by rote or by immersion in writing and reading experiences.

Spelling is learned through:

  • the strategic use of knowledge about
    • Phonology – sound structure
    • Orthography – written symbols to represent spoken language
    • Morphology – smallest parts of words that carry meaning
    • Etymology – origin of words
  • visual activity – memory
  • metalanguage
    • phoneme
    • syllable
    • affixes
    • morpheme – units of meaning, base, root words, prefixes, suffixes
  • spelling system
  • generalisations
  • integration with the teaching of phonological awareness, phonics, word study, vocabulary, writing and reading.

Components of Phonological Awareness:

A Comprehensive Model of Spelling for Educators

Motivation and willingness to engage is influenced by quality of the learning environment, characterised by:

  • meaningful
  • ‘real life’ significance
  • reasonable level of challenge

Instruction needs to:

  • be related to writing and it’s role in effective communication.
  • involve students in group work
  • involve solving word problems
  • build a community of spellers who know how to research and use words for authentic purposes
  • see the teacher taking an important role in modelling and inspiring a passion about words and their value as tools for communication

Differentiation will be needed to meet the students’ range of needs.

“It would be a waste of everybody’s time if they were all expected to learn the same words, strategies and skills.”

To differentiate consider:

  • readiness
  • interest
  • learning profile

To assess readiness the Words Their Way test can be used as a pre-assessment.

Content

  • high frequency word lists
  • words of interest to student
  • words that the teacher has noticed the student trying to spell in writing
  • words that contain features that the students needs to practise
  • words from topics that are being covered across the curriculum

“Having students work through a commercial workbook, at their own pace, does not constitute differentiated teaching.”

 

7 Goals for Differentiation in the Classroom – Heacox 2002

  1. Develop challenging and engaging tasks for each learner.
  2. Develop instructional activities based on essential topics and concepts, processes and skills, and differentiated ways of displaying learning.
  3. Provide flexible approaches to content instruction and products.
  4. Respond to students’ readiness, instructional needs, interests, and learning preferences.
  5. Provide opportunities for students to work in various instructional formats.
  6. Meet curriculum standards and requirements for each learner.
  7. Establish learner-responsive, teacher-facilitated classrooms.

Recommended sequence for teaching sound-letter correspondence.

Spelling Sequence 1

Spelling Sequence 2

Sources of Knowledge

Phonological Knowledge

  • syllables
  • rhyme
  • onset-rhyme
  • phonemes
  • phonemic manipulation
  • word pronumciation
  • segmenting words into syllables, phonemes or morphemes

Orthographic Knowledge

  • sound-letter relationship
  • common spelling patterns/ letter sequences
  • rules for positioning of letter in words

Morphological Knowledge

  • free and bound morphemes
  • root and base words
  • prefixes and suffixes; included inflected endings
  • word derivations
  • rules and generalisations regarding adding suffixes
  • compound words
  • homonyms

Suggested sequence for introducing morphemes Table 4.4 page 76

Visual perception problems

http://www.thevisiontherapycenter.com/discovering-vision-therapy/bid/81695/Spelling-Difficulties-in-Students-Caused-by-Vision-Problems

Word Consciousness

  • interested in words
  • being aware of words and their parts
  • curious and motivated to learn

Spelling is a thinking process not a rote learning task.

Spelling Strategy posters:

  • Sound it out
  • Does it look right?
  • Spell by meaning
  • Consulting an authority
  • Analogy
  • Spell by rule
  • Mnemonics

Technology based interventions:

  • Phonics Alive – Advanced Software
  • Clicker Phonics
  • Fast Forward – (Fairly costly but developed by neuroscientists)
  • Aerobics by Houghton Mifflin Harcourt
  • Wordshark 5 by White Space Ltd
  • Apps
    • Hearbuilder
    • Prof’s Phonics 1
    • Alpha Writer
  • Plickers – using a game called ‘You can join my game’

Use data about where your students are at to determine needs and address these.

Assessment is an important tool to do this.

Explicit teaching of

  • Language
    • phoneme
    • syllable
    • morpheme
    • suffix
    • affix
    • baseword
    • prefix
    • rootword
    • compound
    • homophone
    • homonym
  • Strategies
  • Phonological Knowledge
  • Orthographic Knowledge
  • Morphological Knowledge
  • Etymological Knowledge

Summary:

Characteristics of effective Spelling instruction:

  • Regular assessment – data analysis indicating growth
  • Differentiated practices
    • word lists
    • choices in activities/ ways of working depending on needs and interests
  • Goal setting and regular monitoring with high student involvement in these processes
  • Metalanguage developed
  • Students increasingly developing vocabulary to describe strategies and thinking processes used
  • Learning applied to writing
  • Sense of fun, wonder, challenge experienced
  • Games, challenges as a class
  • Curriculum standards addressed and achieved
  • students increasingly able to articulate their learning, explaining patterns and generalisations and appropriately applying these
  • Evidence shows development – what students say, write, do and make reflected on skills/ knowledge continuum (may not be linear)
  • Intervention strategies implemented for cohorts/ individuals as necessary with support of SSO, parent, peer tutor, regular time with the teacher – tied to goals which are time bound and reviewed to measure effectiveness of processes used.
  • Further assessment sought/ referred if intervention not successful
    • technological tools could be useful (Phonics Alive, Apps, Text to speech (coping strategy)
  • Students use their knowledge and skills strategically to spell increasingly proficiently
    • phonological knowledge
    • orthographical knowledge
    • morphological knowledge
    • etymological knowledge
    • apply strategies for how to spell unknown words
      • sound
      • sight
      • meaning
      • rules
      • mnemonics
      • authority

Phonological and Morphological suggested sequence

Which ‘Characteristics of effective Spelling instruction’ are evident here?