Presentation on theme: "Strategies that Work Teaching for Understanding and Engagement"— Presentation transcript:
1Strategies that Work Teaching for Understanding and Engagement Maths & ComprehensionModule 11Debbie Draper
2We recognise Kaurna people and their land Acknowledgement of CountryWe recognise Kaurna people and their landThe Northern Adelaide Region acknowledges that we are meeting on the traditional country of the Kaurna people of the Adelaide Plains. We recognise and respect their cultural heritage, beliefs and relationship with the land. We acknowledge that these beliefs are of continuing importance to the Kaurna people living today.
3NAR Facilitator Support Model – Team Norms Be prepared for meetings and respect punctualityBe open to new learningRespect others opinions, interact with integrityStay on topic, maintain professional conversationAllow one person to speak at a time and listen activelyEnable everyone to have a voiceDiscuss and respect diversity and differing views in a professional manner and don’t take it personallyAccept that change, although sometimes difficult, is necessary for improvementBe considerate in your use of phones/technologyBe clear and clarify acronyms and unfamiliar terms. Ask if you don’t understand.Commit to follow through on agreed actionRespect the space and clean up your area before leaving
4Overview Mathematics Teaching – research findings Mathematics and Integral LearningComprehension Strategies applied to Mathematics
5Adapting Reading Strategies for Teaching Mathematics K-6 Arthur Hyde Comprehending Math:Adapting Reading Strategies forTeaching Mathematics K-6Arthur HydeBuilding Mathematical Comprehension:Using Literacy Strategies to Make MeaningLaney Sammons
7Readers draw upon Content knowledge Knowledge of text structures Pragmatic knowledgeContextual knowledgeContent knowledge – a foundation upon which to buildPragmatic – how they have solved problems beforeContextual – culture of mathematics learning, teachers’ attitude etc.
8Mathematics and Comprehension In order to understand what the question is asking students to do, reading and comprehension skills need to be developed.Reading requires skills in code-breaking; i.e., knowing the words and how the words, symbols and pictures are used in the test genre.Comprehension--i.e., making meaning of the literal, visual and symbolic text forms presented--requires students to draw on their skills as a text user, a text participant and a text analyst (Luke & Freebody, 1997).Cracking the NAPLaN Code, Thelma Perso
9Mathematics and Comprehension There are many different codes in mathematics that children need to crack if they are to have success with the NAPLAN test genre. These include:English language words and phrases (e.g. wheels in the picture)words and phrases particular to mathematics (e.g., number sentence, total)words and phrases from the English language that have a particular meaning in the mathematics context but that may have a different meaning in other learning areas (e.g., complete)symbolic representations which for many learners are a language other than English - these include "3" representing "three," "x" representing "times," "multiply" and "lots of," "=" representing "is equal to.“images, including pictures/drawings, graphs, tables, diagrams, maps and grids.
10ComprehensionThere are many different codes in mathematics that children need to crack if they are to have success with the NAPLAN test genre. These include:drawings and images (such as the picture of the tricycles) to help them visualise and infer what the question might be askingwords like "complete" and "total number of" to infer what the question is asking; and they alsotranslate from the drawing to the sentence and then to the symbolic representation to understand they need to "fill in the empty boxes."
11ComprehensionThese comprehension strategies need to be explicitly taught and deliberately practiced. Strategies include:experiences with the test genrerelating the text types (drawings, grids, word sentences) to children's experiencesasking children to retell the situation that is being represented and describe or explain to others what they are inferring and thinking about a situation.
12Text StructureStructure of word problems in mathematicshandout
15VocabularyWords that mean the same in the mathematical context e.g. dollar, bicycleWords that are unique to mathematics e.g. hypotenuse, cosineWords that have different meanings in mathematics and everyday use e.g. average, difference, factor, tablehandout
16Effective Vocabulary Instruction does not rely on definitionsrelies on linguistic and non-linguistic representationsuses multiple exposuresinvolves understanding word parts to enhance meaninginvolves different types of instruction for different words (process vs content)requires student talk and play with wordsinvolves teaching the relevant wordsMarzano, 2004
20Confusion... Move the decimal point Just add a zero Times tables Our number systemEleven (should be tenty one)Twelve (
21Overview Theory Conceptual Connections Importance of Research VisualisationResearchOverviewPracticalStrategiesAttitudesPracticeMakingConnections
22Understanding why is important to me. I need to visualise and connect. The theory of mathematics is important to me. I like to know what experts know.Understanding why is important to me. I need to visualise and connect.I like knowing the process and practising problems to get better.I need to know how it is relevant to my life. I like to be able to discuss different ways of solving the problem.
23Your story Consider your educational experiences in mathematics Share with people at your tableBe ready to share with the whole group
39Revoicing - “You used the 100s chart and counted on?” Rephrasing - “Who can share what ________ just said, but using your own words?”Reasoning - “Do you agree or disagree with ________? Why?”Elaborating - “Can you give an example?”Waiting - “This question is important. Let’s take some time to think about it.”
40History of Mathematics 7:04 http://www.youtube.com/watch?v=wo-6xLUVLTQ
44Modelled:Using think alouds, talk to students about the concept of “schema”.When I think about “million” here are some connections I have made:with my lifewith maths that I know aboutwith something I saw on TV, newspaper etc.
45Shared:Use a “schema roller” or brainstorm to elicit current understandings. Ask students to add their ideas.Record on anchor chart.
46Making Connections (Maths to Maths) Concepts are abstract ideas that organise informationQuantityShapeDimensionChangeUncertainty
50Imagine that you work on a farm Imagine that you work on a farm. The owner has 24 sheep tells you that you must put all of the sheep in pens. You can fence the pens in different ways but you must put the same number of sheep in each pen. What is one way you might do this? How many different ways can you find?
51Making Connections Maths to Self What does this situation remind me of?Have I ever been in a situation like this?Maths to MathsWhat is the main idea from mathematics that is happening here?Where have I seen this before?Maths to WorldIs this related to anything I’ve seen in science, arts….?Is this related to something in the wider world?
52What do I know for sure? K. W. C. Imagine that you work on a farm. The owner has 24 sheep tells you that you must put all of the sheep in pens. You can fence the pens in different ways but you must put the same number of sheep in each pen. What is one way you might do this? How many different ways can you find?
53What do I want to work out, find out, do? Imagine that you work on a farm. The owner has 24 sheep tells you that you must put all of the sheep in pens. You can fence the pens in different ways but you must put the same number of sheep in each pen. What is one way you might do this? How many different ways can you find?
54Are there any special conditions, clues to watch out for? C. Imagine that you work on a farm. The owner has 24 sheep tells you that you must put all of the sheep in pens. You can fence the pens in different ways but you must put the same number of sheep in each pen. What is one way you might do this? How many different ways can you find?
55Students need to be able to make connections between mathematics and their own lives. Making connections across mathematical topics is important for developing conceptual understanding. For example, the topics of fractions, decimals, percentages, and proportions san usefully be linked through exploration of differing representations (e.g., ½ = 50%) or through problems involving everyday contexts (e.g., determining fuel costs for a car trip).Teachers can also help students to make connections to real experiences. When students find they can use mathematics as a tool for solving significant problems in their everyday lives, they begin to view the subject as relevant and interesting.
58Questioning Common question in mathematics are... Why do I have to do this?What do I have to do?How many do I have to do?Did I get it right?Common question in mathematics should be..How can I connect this?What is important here?How can I solve this?What other ways are there?
59Death, Taxes and Mathematics There are two things in life we can be certain of.....Death, Taxes and MathematicsAt least 50% of year 5’s hate story problems. They come to pre-school with some resourceful ways of solving problems e.g. dividing things equally. Early years of schooling – must do maths in a particular way, there is one right answer, there is one way of doing it. They are told what to memorise, shown the proper way and given a satchel full of gimmicks they don’t understand.
60Story ProblemsJust look for the key word (cue word) that will tell you what operation to use
63Fundamental Messages Don’t read the problem Don’t imagine the solution Ignore the contextAbandon your prior knowledgeYou don’t have to readYou don’t have to thinkJust grab the numbers and compute!
64Why might this problem be difficult for some children?
65Ben has 2 identical pizzas. He cuts one pizza equally into 4 large slices.He then cuts the other pizza equally into 8 small slices.A large slice weighs 32 grams more than a small slice.What is the mass of one whole pizza?grams
66Newman's promptsThe Australian educator Anne Newman (1977) suggested five significant prompts to help determine where errors may occur in students attempts to solve written problems. She asked students the following questions as they attempted problems.1. Please read the question to me. If you don't know a word, leave it out.2. Tell me what the question is asking you to do.3. Tell me how you are going to find the answer.4. Show me what to do to get the answer. "Talk aloud" as you do it, so that I can understand how you are thinking.5. Now, write down your answer to the question.
67Reading the problemReadingComprehending what is readComprehensionCarrying out a transformation from the words of the problem to the selection of an appropriate mathematical strategyTransformationApplying the process skills demanded by the selected strategyProcess skillsEncoding the answer in an acceptable written formEncoding
68Ben has 2 identical pizzas. He cuts one pizza equally into 4 large slices.He then cuts the other pizza equally into 8 small slices.A large slice weighs 32 grams more than a small slice.What is the mass of one whole pizza?grams
69Read and understand the problem (using Newman's prompts) Teacher reads the word problem to students.Teachers uses questions to determine the level of understanding of the problem e.g.How many pizzas are there?Are the pizzas the same size?Are both pizzas cut into the same number of slices?Do we know yet how much the pizza weighs?
71What do I want to work out, find out, do? C.What do I know for sure?What do I want to work out, find out, do?Are there any special constraints, conditions, clues to watch out for?
72Problem Solving Questions What is the problem?What are the possible problem solving strategies?What is my plan?Implement the planDoes my solution make sense?Up to 75 % of time may need to be spent on this stageK.W.C.
73Ben has 2 identical pizzas. He cuts one pizza equally into 4 large slices.He then cuts the other pizza equally into 8 small slices.A large slice weighs 32 grams more than a small slice.What is the mass of one whole pizza?grams
81One of the main aims of school mathematics is to create in the mind’s eye of children, mental objects which can be manipulated flexibly with understanding and confidence.Siemon, D., Professor of Mathematics Education, RMIT
88Subitising (suddenly recognising) Seeing how many at a glance is called subitising.Attaching the number names to amounts that can be seen.Learned through activities and teaching.Some children can subitise, without having the associated number word.
90MAKE TO TENBeing able to visualise ten and combinations that make 10
91DOUBLES & NEAR DOUBLESBeing able to double a quantity then add or subtract from it.Counting on from the largest is only useful for small collectionsDoubling is one of the first strategies children developWe can explicitly teach doubling as a strategy from early agesDoubling can be used as a strategy to solve problems. (if I know five and five is ten how can I use this to solve seven and seven)
93Imagine that you work on a farm Imagine that you work on a farm. The owner has 24 sheep tells you that you must put all of the sheep in pens. You can fence the pens in different ways but you must put the same number of sheep in each pen. What is one way you might do this? How many different ways can you find?
94Making the LinksAre we giving students the opportunity to make the links between the materials, words and symbols?MaterialsSymbolsWordsThink BoardPicture
98Number of sheep in each pen Number of pensNumber of sheep in each pen1242123846
99Number of sheep in each pen Number of pensNumber of sheep in each pen1242123846
10024 2 columns 12 rows equal factors row column arrays quantity total 1 x 24 = 242 x 12 = 243 x 8 = 244 x 6 = 246 x 4 = 248 x 3 = 2412 x 2 = 2424 x 1 = 24One factorThe other factor1242123846
101Julie bought a dress in an end-of-season sale for $49. 35 Julie bought a dress in an end-of-season sale for $ The original price was covered by a 30% off sticker but the sign on the rack said, “Now an additional 15% off already reduced prices”. How could she work out how much she had saved? What percentage of the original cost did she end up paying?
126InferenceSometimes all of the information you need to solve the problem is not “right there”. What You Know + What you Read ______________ Inference
127What I Read: There are 3 people. What I Know: Each person has 2 feet. There are 3 people sitting at the lunch table.How many feet are under the table?What I Read: There are 3 people.What I Know: Each person has 2 feet.What I Can Infer: There are 6 feet under the table.
128Fact or InferenceThere are 0.3 g fat in 100 g of the soupThe soup is 0.6 % proteinOne serve of the soup contains 450 kJThere is more fat than salt in the soupThere are 3 fresh tomatoes in each can of soupIn each serve of soup there is 20.7 g of carbohydrate
129Read the question aloud Ask students whether there are any words they are not sure of. Explicitly teach any words using examples, pictures etc.Does Peta keep any plums for herself?Ask students to paraphrase the question
130Ask students to make connections –have they shared something out when they are not sure how it will work out? Have you seen a problem like this before? When might this happen in real life?What might the answer be or NOT be? Why?Ask students to agree or disagree and explain why.
131Re-read the information Re-read the information. Peta has some plums – we need to work out how many plums Peta has. Peta is giving some plums to her friends . We don’t know how many friends Peta has.What else do we know and not know?What can we infer?
132If she gives each friend 4 plums, she will have 6 plums left over What can you infer from this?
136Determining Importance Some students cannot work out what information is most important in the problem. This must be scaffolded throughexplicit modellingguided practiceindependent work
137Solve this!Nathan was restocking the shelves at the supermarket. He put 42 cans of peas and 52 cans of tomatoes on the shelves on the vegetable aisle. He saw 7 boxes of tissues at the register. He put 40 bottles of water in the drinks aisle. He noticed a bottle must had spilled earlier so he cleaned it up. How many items did he restock?
138Strategy 42 cans of peas 52 cans of tomatoes tissues at the register 40 bottles of waterwater that he cleaned upimportantnot important
141Summarising & Synthesising Journaling gives students an opportunity to summarise and synthesise their learning of the lesson.Use maths word wall words to scaffold journaling. Include words like “as a result”, “finally”, “therefore”, and “last” that denote synthesising for students to use in their writing. Or have them use sentence starters like ”I have learned that…”, “This gives me an idea that”, or “Now I understand that…”
142K. W. C. What do I now know for sure? How can I use this knowledge in other situations?What did I work out, find out, do?How did I work it out?Were there any special conditions?What conclusions did I draw?
143What facts did I learn?How did I feel?What went well?What problems did I have?What creative ways did I solve the problems?What connections did I make?How can I use this in the future?
144Journal What is Draw it the rule? What connections do I know? Show an exampleHow does itrelate tomy life?
145Journal A = L X W Area equals length multiplied by width Multiplication factsArrays and gridsOne surface of some solids e.g. cylinderSame as 2 equal right angled trianglesA = L X WArea equals lengthmultiplied by widthJournalA room has alength of 4 metresand width of3 metres.The area is4m x 3m = 12 sq metresMeasuring materialfor a tableclothWorking out how manyplants for my vegetablegarden
147We now know a lot more about how children learn mathematics. Meaningless rote-learning, mind-numbing, text-based drill and practice, and doing it one way, the teacher’s way, does not work.Concepts need to be experienced, strategies need to be scaffolded and EVERYTHING needs to be discussed.