A repertoire of sentence strategies

Sentence Work Routines

Following my thinking on the because-but-so strategy, I thought it would be useful to consider what my repertoire of strategies for teaching syntax should be this year.  I think the benefit of focusing on sentences is that it provides a focus on both reading and writing.  I think it’s really important that children understand how the structure of a sentence and the particular words that are used, indicate a specific meaning.  The more children understand this meaning, the stronger their command of English will be.  That said, I know that I also have some more thinking to do about teaching at the text level, but I think good sentence structure should be the first focus.

The following activities are taken from my reading of Judith Hochman’s work; however, there are many similarities with suggested activities found across a range of teacher education literature and the internet.  In this blog, I’m going to add my own reflections on why I think they will be useful and when they could be used effectively.  From the outset, I think that using these activities across the curriculum, perhaps in starters, activities or plenaries, would be remarkably beneficial to develop knowledge, reading and writing simultaneously.

Strategy: Sentence Fragments

Description: Take a fragment of a sentence and add extra information to create a complete sentence.  It would also be useful to provide a paragraph and children need to find the fragment or run-on sentence – perhaps before an editing lesson.

Example: the people at Hampton Court -> The people at Hampton Court were less friendly than William had hoped.  or -> William disliked the people at Hampton Court.

Develops: This strategy develops the notion of a sentence – subject and verb, punctuation, clause etc – and supports children’s ability to fix their own writing.  It would be very useful to compare complete sentences with fragments to develop the concept of a sentence.  Moreover, it forces them to make connections by expanding ideas, thereby developing knowledge and understanding at the same time.

Strategy: Sentence Types

Description: Write, or rephrase, a sentence in one of the four sentence types.

Example: Rephrase “Henry VIII had six wives.” as a question sentence. or Use the word reformation in a statement, question and exclamatory sentence.

Develops: This strategy can be used to revise and practise particular sentence types.  It focuses on the function of a sentence.  Furthermore, it also offers an opportunity to deepen vocabulary knowledge.  Moreover, generating questions is a very worthwhile activity in itself.  Answers could be provided for children to design questions for, and then children could make progress by generating their own questions after reading a text.

Strategy: Sentence Combining

Description: Choose a conjunction to join two clauses.

Example: Choose a conjunction from although/while/however* to join the following clauses together: William went to London.  He did not meet the King for months.  *this would test pupils’ knowledge that however can’t be used to join two clauses in one sentence.

Develops: I remember being told that this was one of the most effective strategies for teaching grammar.  This strategy develops children’s understanding of the meaning of conjunctions in demonstrating the relationship between two clauses.  It also provides a feel for more complex sentences, which develops writing.

Strategy: Appositives

Description: An appositive is a word or phrase that has the same meaning as another in the sentence or paragraph e.g. my teacher, Mrs Miller or  Anne Boleyn, the second of Henry VIII’s wives.  Children should practise writing sentences to include an appositive or be given two appositives to write a sentence about.  Additionally, children could design their own appositives for their writing (practising creating expanded noun phrases).

Example: Add an appositive to this sentence: Catherine of Aragon did not bear a son. or Write a sentence using these appositives: Edward   King Henry VIII’s only son.

Develops: This supports reading in that embedded clauses, where appositives are often found, are often tricky for children to understand.  Furthermore, it provides opportunities to write with more sophistication, variety and cohesion.

Strategy: Extending sentences

Description: A very short, simple sentence is provided and children add information such as who, what, when, where, how or why.  The when, where, how and why would be particularly useful for KS2.

Example: Extend this sentence: William ran. ->

William ran to the castle.

William ran after hearing his name being bellowed.

William ran hurriedly.

William ran so that he would not upset the King.

Then, children can put this all together: After hearing his name being bellowed, William ran hurriedly to the castle so that he would not upset the King.

Develops: This supports children’s facility with extending sentences.  I would see this as being particularly useful when editing work and teaching children how to extend their ideas particularly for those children who struggle with writing.

Strategy: Appositives

Description: An appositive is a word or phrase that has the same meaning as another in the sentence or paragraph e.g. my teacher, Mrs Miller or  Anne Boleyn, the second of Henry VIII’s wives.  Children could practise writing sentences to include an appositive or be given two appositives to write a sentence about.  Additionally, children could design their own appositives for their writing (practising creating expanded noun phrases/finding synonyms).

Example: Add an appositive to this sentence: Catherine of Aragon did not bear a son. or Write a sentence using these appositives: Edward   King Henry VIII’s only son.

Develops: This supports reading in that embedded clauses, where appositives are often found, are often tricky for children to understand.  Furthermore, it provides opportunities to write with more sophistication, variety and cohesion.  This strategy draws together content knowledge, be that of a text, idea, event or concept.  Matching appositives might be the first step in this strategy, and then children can develop their own alternate phrases for nouns.  This would be a rich task for developing expanded noun phrases, cohesion and punctuation.  For example:

Adolf Hitler      a cruel, abhorrent man     the cruel, evil dictator

the Blitz a storm of gun-fire and bombs

It could lead on to more sophisticated noun phrases which might be used across two sentences, rather than in the same one:

whole and part:

rations / the flour

They collected their rations.  There wasn’t much flour.

item and container:

orange juice / the bottle

John asked for some orange juice.  His sister handed him the bottle.

item and hyponym:

two coffees / the drinks

Jill ordered two coffees when she arrived.  Unfortunately, she waited over five minutes for her drinks.

This explicit focus must also develop reading as these references are potentially confusing for children who fail to make a mental model of the text.

Strategy: Scrambled sentences

Description: The words in a sentence are mixed up and children must piece the sentence back together again.  The first word of the sentence could be emboldened as a scaffold.

Example: founded / from / broke / Pope / away / VIII / the / the / King / of / England. / Henry / and / Church

Develops: This develops content knowledge and understanding of syntax.  The complexity of the sentence is important, as clause structures mean that a correct sentence could be made that is different from the teacher’s original version.

Strategy: Subordinating Conjunctions

Description: Children complete a sentence starting with a subordinating conjunctions.  There are a few variations on this strategy, shown in the examples below:

Example:

Finishing a subordinate sentence stem (to check comprehension and understanding)

After divorcing Catherine of Aragon, ___________________________.

Completing a subordinate clause, given a main clause (to check comprehension and understanding):

Before ______________________________, King Henry VIII was named Defender of the Faith.

Writing a sentence beginning with a subordinate clause:

If  _____________________________________________________________

Completing sentences with different subordinating conjunctions (to develop an idea)

Before Henry VIII founded the Church of England, _______________________________.

After Henry VIII founded the Church of England, _______________________________.

Although Henry VIII founded the Church of England, _______________________________.

When Henry VIII founded the Church of England, _______________________________.

Develops: This develops content knowledge and understanding of syntax: in particular, the relationships demonstrated by conjunctions.  It also supports more sophisticated writing, in addition to testing comprehension and understanding.  Furthermore, it provides practice of writing with different clause structures.  Challenge could be provided by combining the latter example with appositives e.g. After Henry VIII founded the Church of England, the rebellious, unforgiving king ordered the massacre of many Catholics.

Summary

I think that using these strategies as a repertoire of sentence level teaching strategies will bring about some important benefits.

Firstly, children will soon learn the expectations of particular strategies which means that the “how to” of the task will not interfere with the intended learning once pupils are used to them.

Secondly, the practising of particular strategies provides explicit strategies for writing upon which children can call.  This means that children will be able to employ particular strategies for particular reasons.

Thirdly, using these sentence level activities across the curriculum means that English is being taught throughout the day.  The content of the sentences reinforce the content knowledge of the subject, making the usage of these activities effective use of teaching time.

I’m looking forward to reflecting on these strategies and their effects during the first half term back at school.  As always, I’d welcome and feedback on the ideas in this blog post and would love to hear of any ideas that would contribute towards this thinking.

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A Focus on Conjunctions

Developing Grammar, Knowledge and Writing in One Teaching Strategy

Last week, I came across a blog referring to the Hochman Method of teaching writing.  I had never heard of it before so started to do some research on the web (there is a book called ‘The Writing Revolution’, but my book allowance has ran out for August).  Sources on the web describe several strategies which can be used to develop children’s sentence writing skills.  One which caught my attention, and which is the focus of this blog, is a strategy called “Because – But – So”.

The “Because – But – So” teaching strategy develops children’s ability to write complex sentences.  After learning about an idea, event or concept, children complete three sentences using the conjunctions listed in the strategy.  Children are presented with the same sentence stem such as “Henry VIII wanted a male heir” but must adapt the next clause to reflect the relationship signalled by the conjunction.

For example:

Henry VIII wanted a male heir because he did not think a female heir could rule the kingdom. (The subordinate clause explains)

Henry VIII wanted a male heir, but his first wife had a girl. (The clause adds a change in direction)

Henry VIII wanted a male heir, so he divorced Catherine of Aragón.  (The first clause provides a cause and the second clause provides an effect).

The task is not as easy to design as it would first appear.  All of the second clauses must be possible, and children must have, or have had, access to suitable knowledge.  Provided this is the case, the task then develops several skills both explicitly and implicitly:

  • children make connections between pieces of knowledge and how they relate – this develops their schema of the topic;
  • children develop understanding of sentence structure and punctuation which should then be transferred into their own writing when provided with opportunities to do so and after sufficient practice;
  • children develop an understanding of grammar; each of the conjunctions signify different relationships between clauses.  This supports both comprehension and command when writing.

Ideas this sparked

I really like the possibilities of this simple yet potentially very effective strategy.  As long as children are shown how to construct these types of sentences well, the rigour embodied in the task should enable them to develop their content knowledge, relational understanding, sentence structure, punctuation and comprehension all in the same task.  I would very much like to incorporate such a task as daily sentence level work given its richness.  Daily practice of such sentence writing would provide important sentence writing practice, but also opportunities to recall and consider subject knowledge.  I think this represents very good use of teaching time.

Developing vocabulary knowledge depth

Another possibility for this strategy is how it could be used to develop vocabulary knowledge.

For example, consider how this strategy develops a depth of understanding around the word “grieving” in addition to providing an opportunity for children to practise retrieval or inference making from the text (in this case, “Treason” by Berlie Doherty):

William’s father was grieving because Matthew had drowned.

William’s father was grieving, but he did not cry.

William’s father was grieving, so he stopped talking to William.

The above example would probably be quite difficult for some of the children in my class next year, but that should not stop me aspiring to get them to this level.  I think that effective and regular modelling and sharing of these sentence types would support children’s understanding of the type of information that would follow each conjunction.

Developing use of conjunctions

I have wondered for a long time about how conjunctions should be introduced to children.  It is probably something that is quite implicit, developed through reading.  I’m becoming more of the opinion that little can be left to be developed implicitly for some of our children, and so I think that this strategy could also be adapted to introduce, or practise the use of, other conjunctions.  I think it’d be particularly useful to start with some conjunctions which signified similar relationships.

For example:

Causal:

Brother John spoke with William since he wanted to help him.

Brother John spoke with William as he wanted to help him.

Brother John spoke with William for he wanted to help him.

and then move on to more complex relationships between clauses:

Contradictory or concessionary:

Brother John spoke with William although William had his mind on other things.

Brother John spoke with William whereas William had his mind on other things.

Brother John spoke with William even though William had his mind on other things.

Brother John spoke with William in spite of the fact that William had his mind on other things.

Conditional

It was difficult to survive in the Tudor times if you were poor.

It was difficult to survive in the Tudor times unless you were rich.

It was difficult to survive in the Tudor times even if you were loyal to the king.

Time/Sequential

William studied Latin before he became the king’s favourite.

William studied Latin after he had mastered French.

William studied Latin until he was sent away.

William studied Latin when Father John was his teacher.

William studied Latin as soon as he started school.

William studied Latin whenever he had the chance.

William studied Latin while he attended Father John’s school.

This approach would introduce a range of conjunctions for children to use in their own writing, but do so in a way which helps develop their understanding of their nuanced differences in meaning as well as providing excellent opportunities for discussion.  Children could discuss how the conjunction adapts the relationship between the two clauses, which then supports more appropriate usage in their writing and in comprehension when reading.

Conjunctive Adverbs

Once children are secure in a range of conjunctions, the strategy could evolve into the use of conjunctive adverbs.  This would provide a writing frame for correct punctuation and syntax.

William became the King’s favourite. However, he still felt wary of others at court.

William became the King’s favourite. In contrast, others at court considered him less favourably.

William became the King’s favourite. Beforehand, William was rather fearful of him.

William became the King’s favourite. Moreover, King Henry presented him with his own horse.

Again, discussion around tone and impact of sentences could follow such an exercise which would develop children’s ‘feel’ for language (tone, formality etc).  For example, I would start a discussion on the effect of ‘in contrast’ and how it does not sound like it belongs in a story.  Additionally, I would also want to explore how to use a semi-colon in the above examples depending on the connection between the ideas.  This would train children to place a semi-colon correctly and use it with purpose.  When children are ready for it, further discussion could happen around the placing of the conjunctive adverb in the second sentence.

For example, children could think about the effect of placing the adverb at the beginning, middle or end of the sentence:

William became the King’s favourite. However, he still felt wary of others at court.

William became the King’s favourite. He still felt, however, wary of others at court.

William became the King’s favourite. He still felt wary of others at court, however.

Summary

I’m looking forward to incorporating these ideas into daily sentence work once we return back to school.  I’m hopeful that this approach will bring improvements in children’s knowledge, syntax, grammar, comprehension and communication.  I think that through explicit teaching, children will become better crafters of writing in that they will learn how to communicate relationships between ideas.  Once they leave primary school, this will leave them in good stead to read and write more analytically in Key Stage 3 and beyond.

Maths Reasoning and Pupil Voice Part 2

Yesterday I was able to sit with a few of my learners to discuss their approaches to some of the reasoning questions.  Whilst some of my initial hypotheses were correct about why some low scores were attained – not reading the question properly being the top one – it was a useful exercise in gaining insight about the children’s approaches.

I interviewed four pupils who all scored below ten on the KS2 Mathematics Reasoning Paper 3 2016.  Their scores ranged from 1/35 to 9/35.  Their procedural fluency scores were higher with a range of 12/40 to 27/40.  These scores would render these children working below Year 6 standard, if they were the actual results in May.

“I read it through and didn’t get it”

shay

This response to the above question was quite straightforward, but it made me think of the emotional response in addition to the cognitive response.  Compared to the previous question, which the pupil knew he could do because he “knows time”, I wonder how a lack of confidence with this non-routine problem affected his potential to attack the question. With guidance from me prompting him to look for certain information and a scaffold for how to re-represent the problem, there were no arithmetic barriers and he was successful.  This suggests that the children need a richer diet of problems to build experiences which will support them in the SATs.  In addition, perhaps another pedagogic implication is to plan for individual thinking time, before collaborative working, when dealing with problems in class so that I can more easily identify which pupils rely on others more.

“Reading the protractor made it difficult”

Jaccob angles.png

This response showed that the pupil was confused between the different directions of the protractor.  He did not score on this question at all, and yet independently defined acute and obtuse for me and was able to identify, without a protractor, which angles were acute and obtuse.  This implies that he, and perhaps others, need to be build confidence in their capabilities and be more reliant on checking strategies.

“I thought the answer was too big”

jaccob marbles.png

The pupil achieved the correct answer in his working out but did not write it in the answer box. He explained that he thought it was too big an answer.  This was an interesting response and I suggest that more experience of problems involving “larger” answers would support this pupil.  Kudos to him for considering how likely the answer was – showing he is thinking about what he is doing.

“I thought smallest means the least digits”

lewis

This pupil applied the wrong strategy despite practising a very similar question days before our practice paper.  He explained that the language was confusing.  Given the pupil’s history, language is an issue – however, it shows that providing experience with these type of problems cannot be taken for granted that they will prepare the children for similar problems in the future.  It shows for these children who score poorly, I need to have a stronger focus on them explaining or proving that they understand why they have answered the question in this way – especially if they have worked with a partner.  This ‘explanation’ will be better feedback for me than the response by itself

Summary

This was a really useful task, and one which I think I should do more often.  It has given me a real insight into the students’ approaches and has allowed me to get to know the pupils better.  The implications for preparing these pupils for success are:

  • Insist on explanations for answers in lessons
  • Ensure that collaborative learning tasks are structured in ways which allow for individual assessment
  • Provide a broad range of problems to build pupils’ confidence (knew this anyway, but glad to see it is important)
  • Provide instruction on how to re-represent problems to support understanding – bar modelling in particular.
  • Provide more opportunities for children to hear other children’s working out and then attempt strategies themselves.  I am quite interesting in using the Rally Coach Kagan structure for this.

 

Knowledge Organisers in Primary Science

For some time now, I have been really interested by the concept of a knowledge organiser. I first came across this idea on Joe Kirby’s blog a few years ago and have tried over the years to understand how it might be applied to primary (in amongst getting on with the day job and everything else).  More recently I have seen examples of knowledge organisers being used at primary level, and it led me to experiment with creating a few.  This blog is about my thoughts on how I think they might be used and how they might support teaching and learning.

My understanding of a knowledge organiser

A knowledge organiser is a document which details all the important facts and relevant information needed for learners to understand the topic they are learning.  These are listed on a simple document and children are given copies at the start of the unit, encouraged to spend 10 minutes a night reviewing this information, and can be regularly tested on the content in a similar fashion to times tables tests.  They ensure that all members of the school community understand the expectations of what is to be learned in a unit of learning.

Do knowledge organisers represent didactic teaching?

I am certainly not against didactic teaching; I think it is a tool that suits certain situations better than others and can be used very effectively.  My concern would be if only didactic teaching were used in primary science because I think children, like adults, need to encounter concepts in different ways and have multiple experiences with those concepts to truly develop understanding.

I did initially think, perhaps due to my perception of some of the practices at the school where Joe Kirby works, that knowledge organisers represent rote learning.  Having been trained at university by a science department that held at its core a social-constructivist view of learning (as I feel I myself do), I wasn’t sure how I felt about this.  However, I am moving towards the idea that knowledge organisers in their simplicity would provide a grounding in the topic children are learning.  A grounding in vocabulary and facts that children could then use to make sense of more practical and stimulating classroom lessons.

For example, if children came to a science lesson having an awareness of terms such as force, friction, air resistance and gravity, any experiences with parachutes or feathers or hammers or whatever is dropped from a height would then be able to fit into a conceptual framework and develop understanding.  Even if children had no understanding of the definitions they had learned beyond recital, further experiences would then develop this understanding by providing examples and deepening their knowledge.  I would argue that both examples align with a social-constructivist view of learning, where the core knowledge is the starting point and surface knowledge can more readily be established so that deeper understanding can more readily be obtained.  Moreover, if children regularly review knowledge organisers, their understanding of each term would be reshaped and refined as they bring their experiences to their mind whilst revising the core knowledge.

Knowledge organisers as a shared language of learning

What really excites me about knowledge organisers is that the knowledge components of the curriculum can be made visible to everyone: teachers, parents and most importantly pupils.  Moreover, I hope that these components might support subject knowledge for teachers who have not had specialist science training.

Our curriculum has deconstructed the National Curriculum objectives and aligned them to the ASE’s Big Ideas of Science so we have a conceptual curriculum which is progressive in each of the main ideas year-on-year.  The reasons for this were numerous but one key reason was to give teachers autonomy over how they structure science learning in line with the rest of the curriculum – to prevent them from being restricted about what is covered and when, which they might find if we used a scheme of work.  This intended freedom has then created a work-load issue for staff in terms of building content knowledge for each objective.  By specifying the knowledge content of each objective, this will create consistency for all children but hopefully reduce teachers researching time so they can spend more time planning and preparing exciting lessons.

How will knowledge organisers change the format of science lessons?

I envisage that if children review, revise and quiz themselves (using their chrome books) on knowledge components of the curriculum, lessons can be dedicated to developing these ideas through activities which require higher order thinking.  For example, lessons in Year 6 on the circulatory system could be spent comparing the circulatory system and the respiratory system, rather than spending time labelling parts.  Role play of change of state would be more meaningful if children had the language to discuss what their actions actually represented.  If Year 3 learned about the different theories of gravity, not only could they develop the understanding that the scientific view of the world can change, but they can also then spend lessons recreating famous experiments and distilling key aspects of why scientists such as Galileo made the theories he did.  In conclusion, lessons can be more ambitious, challenging and motivating because all children will have the chance to engage in higher order thinking. It goes without saying that this would raise attainment for all pupils, particularly those at risk of underachievement.

Closing thoughts…

I have created 20% of the knowledge organisers for our curriculum and it has taken me about 10 hours in total so far (an example of one for geology is here).  I do not want to be the one to exclusively make them because I value the contribution of others and truly believe the knowledge organisers would be better constructed in collaboration with others.  However, everyone is extremely busy and a start is better than nothing at all.  I want to trial and investigate the impact the knowledge organisers have on science teaching and learning and gather pupil and teacher voice to check how they fit with the many assumptions I am making about the benefits I hope they will bring.  I think all of the important aspects of science teaching – particularly in gathering what children’s pre-existing ideas about concepts are to identify misconceptions which need to be addressed – can sit alongside knowledge organisers, which will provide a consistency and commonality that should increase engagement and attainment.

I would absolutely love and welcome and feedback, thoughts or comments anyone has.

Thanks,

Marc

Maths Reasoning and Pupil Voice – Part 1

Today our Y6 children completed Paper 3 of last year’s maths SATs.  Reasoning has been a focus in every single lesson, every single day since September.  Some children did very well, with around 10% showing achievement within greater depth.  However, the test held deep challenges for many children.

This evening I’m thinking about why some children were completely flummoxed by the questions.  We teach in a very talk-led, collaborative style with children having ample and regular opportunities throughout each and every lesson to discuss their learning and learn with and from each other.  Children demonstrate successful application of their learning with the White Rose Maths Hub activities – which are superb – and teachers assess that the learning has been very successful.  Then, the children sit a SATs paper and for some reason, every ounce of ‘sense-making’ seems to escape.

One of the tasks for my master’s degree was to interview children about a piece of work.  I think rather than trying to use literature to interpret why some children struggle so much in the tests, I will make time next week to interview some of the children who really found this paper difficult.  I’ll have three main questions:

  1. How did the paper make you feel?
  2. What strategies did you think you’d need to use?
  3. What strategies did you use for (a range of questions)?

I’ll post the results next week but I would be very much interested in other Y6 teachers’ experiences and how their children perform in tests in comparison to daily lessons.

Have a great weekend.

Marc

Maths Reasoning, Growth Mindset and Language

After the SATs, I was really bothered about how my teaching impacts children’s ability to reason mathematically.  It felt like we had nailed arithmetic, with historic low-achievers (Level 2As at EOY4) achieving 60% or more on tough practice papers.  However, for reasoning, it was quite a different story.  The challenges of teaching children how to understand and represent mathematical relationships, and teaching the language, preparedness and resilience to reason with them, has been quite significant.  It is an area of my practice that I want to drastically improve and develop next year.

I’ve started off this half term by planning a unit of learning around Algebra, using the planning guidance from the NCETM.  I must say I found the planning process quite lengthy, however it was extremely valuable.  The planning process explores necessary prior knowledge, opportunities for exploration and play, consideration of possible misconceptions and difficult areas to teach, and how children can demonstrate their understanding along their learning journey.

What is the focus of the teaching sequence?

Children are able to represent linear sequences using algebraic expressions; reason with algebraic expressions in a range of contexts; and understand how their understanding of number can help them solve equations.

KEY CONCEPTUAL IDEAS AND MAKING CONNECTIONS

  • What are the steps in understanding needed along the journey?
    • Seeing patterns – numbers, shapes, sounds,
      • Square, triangular, rectangular numbers – Pascal’s Triangle
    • Generalising rules from observed patterns with justification
    • Understanding rules as being recursive or ordinal
    • Representing sequences using algebra – Finding the nth term
    • Representing variables using letters
    • Four operations using variables
    • Proof – use of Sudoku – deductive, counter-example, exhaustion, contradiction
    • Finding the value of variables
  • What is the best way to order these steps?
    As above
  • How are the steps going to be connected?
    Through building on previous steps
  • How is this journey going to be connected to prior learning?
    • Seeing patterns in nature and maths
    • Area/Volume + perimeter
    • Missing number problems

DIFFICULT POINTS

  • What are the common misconceptions within this area?
    • Seeing the = sign as equivalence on both sides
    • Understanding letters to mean numbers
      • Confusing letters with units of measurements
      • Confusing letter with initial of object
      • Not understanding that letters are variables
    • Visualising mathematical structure in word problems
  • Which parts are difficult to teach and difficult to learn?
    • Generalising patterns – conceptual step
    • Understanding variables – children need to see symbols as the pronouns of maths and then substitute symbol for value; then finding values is the reverse and deepens understanding
    • Solving equations with two unknown variables – use Numicon/Cuisenaire to support
    • Visualising mathematical structure in word problems – will need lots of practice and varied representations

REPRESENTATIONS

  • Which models and images will best support understanding of the different parts of the journey?
    • Function machine – representing patterns
    • Matchsticks – representing patterns
    • Square, triangular, rectangular numbers – representing patterns
    • Number squares – representing patterns
    • Numicon – representing and naming patterns finding nth term PPT
    • Tangrams – introducing letters for variables
    • Follow me cards e.g. 3 + x = 7 – introducing letters for variables
    • Bar model/cubes – mathematical structure
  • Which models and images will expose the difficult points and misconceptions and support understanding in these areas?
    • Numicon
  • Which contexts will support the children to make sense of the maths and give the maths meaning and purpose?
    • Patterns in times tables
    • Pascal’s triangle
    • Fibonacci sequence – in nature
    • Playing and representing ‘Nim’
    • Number square
    • Paving slabs around a garden
  • What language will the children be expected to make sense of and use?
    • Next, before, after, first, fifth, repeat, again, continue, guess, check, predict, if, then, so, because, but
    • Variable
    • Equation
  • How will children be expected to represent their thinking and understanding and different points on the journey?
    • Describing patterns
    • Generalising patterns using words and justifications – function machines
    • Recognising different ways of expressing sequences
    • Finding the nth term
    • Balancing equations using the equal sign
    • Calculations using formula – match up the symbols with the activity
    • Developing reasoning through Sudoku – how do you know?
    • Finding the value of variables in different contexts

VARIATION

  • How can variations be used to support the understanding of the structure of the mathematics?
    • Use contexts to support understanding of patterns and variables Days of Christmas (Children compare how they would write and how it is written conventionally; and then set targets/feed forward).
    • Using children’s own ideas about sequences
    • Replacing missing number boxes with different shapes first, then letters
    • Using Numicon and envelopes to work with unknown variables
  • What needs to be varied to expose the difficult points and misconceptions?
    • The side of the equation with the calculation – to support understanding of the equals sign
    • The types of sequencing
    • Representing word problems visually using bar model and then symbolically using algebra
  • How can variation be used to ensure depth of understanding?
    • Using slightly different examples to develop understanding
    • Use examples and non-examples to develop understanding

GOING DEEPER
What opportunities are there for demonstrating creativity and imagination?
What contexts would provide opportunities to explore and generalise about the mathematics at a deeper level
Patterns in times tables

I’ve really enjoyed teaching this unit, and I dare say that the children have enjoyed discovering patterns and finding rules.  What has been challenging but doable, is persuading the children that the wrong answer is equally as important as the right answer, in terms of learning.  We have talked extensively about being in the pit, and how the learning dispositions can help us get out with new learning; extending this metaphor to us being at a higher point in our learning even if all we have found are ‘wrong’ solutions.

This has been achieved through the use of success criteria which provides feedback on reasoning processes such as ‘working systematically’ and ‘making and checking predictions’, in addition to perfecting my poker face so that answers right or wrong are both welcomed in the same way.  Giving children open-ended investigations, along with scaffolding the language of generalising and justifying, has also brought about rewards in making the learning more successful.

There have also been key learning points for me:

  • Language has a vital role in maths reasoning and next year I must develop children’s oracy in mathematics much more deliberately than this year.
  • Patterns exist everywhere in maths, and identifying and continuing patterns is relevant and valuable throughout the year – not just with algebra.
  • Opportunities to develop generalisation and justification capacity must be created across the year, so that children are always thinking mathematically.  For this reason, mathematical reasoning must be the focus of most lessons.  This will enable children to develop their relational understanding.
  • Assessment of how children think about maths is extremely useful for planning.  For example, children who still resort to additive thinking need teaching and training with multiplicative thinking if they are to begin to understand relationships such as ratio, proportion, fractions etc
  • Self-efficacy in maths can be created through use of success criteria of the reasoning thinking processes.  This is a slow process and needs implicit messages to be controlled.  Regular discussion of what it means to be in the pit, using the learning dispositions and celebrating all learning, rather than correct answers, are important tools which can be used to achieve this.

I’m looking forward to increasing my bank of straightforward reasoning tasks which can be used across the maths curriculum, particularly for arithmetic practice and effective starters (in the Shirley Clarke sense of the phrase).  I’m going to try to store them on a Pinterest board as there are so many good ideas out there.

Teaching Morphology – Reading and Spelling

Having recently completed a literature review and evaluation of a morphology intervention on reading and spelling, I’ve decided to blog to share some of my learning and welcome comments and feedback.

What is morphology?

Morphology is the study of word parts.  Teaching morphology can improve reading and spelling as it develops children’s ability to link meaning with orthography.

Morphology and Reading

Morphology can benefit reading in the following ways:

  • Word reading – children will be able to read syllables more automatically e.g. they will recognise affixes such as ‘inter-‘, ‘ment’ or ‘ious’ without needing to decode each sound and blend.
  • Word understanding (grammatical knowledge) – children will be able to use knowledge of affixes to determine the function of the word e.g. words ending in ‘ment’ or ‘ness’ are nouns
  • Children can use their knowledge of root words and affixes to hypothesise about unfamiliar words, using the context of the sentence to check their hypothesis e.g. ‘The crowd erupted with applause.’ erupt = ‘ e(x) [out] + rupt [break] + ed [past tense]’ meaning ‘broke out’ + ‘applause ‘means clapping = The crowd broke out with clapping = The crowd made a lot of noise by clapping.
    Obviously there are some inferences to be made here, but the strategy gives the children a starting point to infer the meaning of the word.
  • Vocabulary size – understanding that affixes and root words can be combined to generate other words means that children can know the meaning of many words without being directly instructed in each one.

Morphology and Spelling

It is argued that English spelling more closely reflects meaning than sounds.  This is in direct conflict with a phonological approach to spelling being taught through phonics in KS1.  Whilst this approach is sufficient as a starting point, it is increasingly insufficient for children learning more advanced vocabulary.  For example ‘sign’ and ‘significant’ both use the root word ‘sign’ yet the root word is pronounced completely differently.  Explicit teaching of how root words retain their spelling, or follow a pattern, when inflected with affixes can support children by providing a wider knowledge of spelling strategies.  This would be particularly useful for children who read less as they are less likely to generalise from reading how inflections affect spelling.

My intervention found that my Y6 pupils had a primarily phonological approach to spelling – to the point that even when all complete the Lexia programme on a daily basis, which teaches children about derivational and inflectional morphology, they have not developed, or are metacognitively aware of, a morphological approach to spelling.

Creating awareness of and developing this key knowledge could support these children to become better readers and spellers.  It is interesting that this approach may be particularly beneficial for dyslexic pupils.

How will this be implemented in my practice?

It’s advised in the literature to use morphological approaches alongside other approaches such as phonological and visual strategies.  From next year, I will teach root words and inflections to children to read and spell new words.  This will require teaching for connections in spelling (relational thinking) and explicit word hypothesising skills in reading.  Additionally, I will teach it as a word reading strategy to improve children’s automaticity and grammatical knowledge.