Hope experienced frustration when her first model wouldn’t stay together because of the more difficult design. She pulled all the pieces apart and decided to start over, making a simpler design that required less blocks and joins. Even though she was upset and frustrated she persisted and tried a new strategy. Students are able to... *WILL BE INCLUDING STUDENT WORK SAMPLES/PHOTOS/VIDEOS UNDER EACH OF THESE HEADINGS. HEADINGS WILL BE SEPARATED ONTO A PAGE EACH. Resilience strategies: Tried another idea (robot fell apart), Broke task into smaller parts (made it in two halves), Keep checking (measuring and counting continuously)
Student examples at the bottom pictures/videos/responses.
Having a sense of purpose means that students are explicit and clear about the reason as to why they are learning the concepts and participating in structured activities. They are aware that there is an outcome that is meaningful to them. So for example, when they needed to construct a house out of blocks, they first needed to plan and build their structure and take a photo of it in order to give it to a buddy to recreate. When beginning to explore fractions, decimals and percents, students brainstormed ideas about where they ‘see’ this type of maths in their everyday lives to begin to think about practical applications of the concepts.
Discovering new information for themselves that are connected to reality Explorations involve complex problem solving situations that are connected to the abstract mathematical concepts. Primary Years: Students are allowed the opportunity to decide which processes they will take, what materials they will use, where they will work and with who, how they will record and explain their discoveries. Junior Primary Years: Open ended process where students have a choice of materials but the possible strategies are modelled and students are guided through their problem solving. The language is explicitly used and taught throughout the thinking process. Results are not the key focus, rather than the process taken. Reflections are focused on not necessarily their ‘answers’ but the strategies they used, obstacles they faced and overcame and what they could try next time. Mathematical discoveries are celebrated daily and students are experiencing fun while learning. They are given the opportunity to be mathematical, without worrying whether or not their answers are correct. Strategies are explicitly spoken about and other people’s ways of working out are considered and shared and at times even copied.
This list of strategies was originally developed and presented to the students and reflected on which strategies they used the most and developed and modified new strategies that they were using that weren’t originally planned for. The language is clearly displayed on a resilience wall in the classroom for students to use and manipulate. Put each one in a separate box and then use two separate working out examples and talk about which ones each student used. One JP and one MP example explaining what they used.
Put student video of problem solving and get people to identify which strategies they can see them using. Whether or not they are showing resilience.
Why focus on MathematicalResilience?Working on the assumption that...mathematical resilience will improve mathematicalachievement.• Students taking a greater responsibility for their own learning – studentsare discovering mathematical concepts rather than just accepting informationthat is passed on• Resilience can be taught and learnt• Resilience positively impacts learners, empowering them and creatingsuccess for all students• It can become a common classroom and school language about learning• Maintains high expectations of all Aboriginal students to achieve• Valuing mathematics and its connection to the world• Learnt skills are transferrable to others areas of learning and also life forfuture learning
Defining mathematical resilienceResilience in general...“Resilience refers to the ability to successfully manage your life andadapt to change and stressful events in healthy and constructive ways”(Dent, M).“An individual’s ability to thrive and fulfil potential despite or perhapsbecause of stressors or risk factors” (Neill, J).How does this connect with mathematical learning and success?“When mathematically resilient pupils are required to use mathematicsin a new situation they will expect to find it hard at first but will havestrategies or approaches to overcome the initial “can’t do it” response”(Johnston-Wilder S & Lee C).
Resilience IndicatorsHow can we identify resilience in students?• Confidence in their own ability to try something new• Sharing their knowledge willingly with others• A range of useful strategies to apply in different situations• Challenging themselves• Solving different problems• Formulating their own questions – identify what they don’t already know andpossible ways to explore this• Identifying what comes next in their learning• Reflecting on their learning and describe the processes that have taken – usingmetalanguage and mathematical vocabulary• Maintaining their attention and focus for longer periods of time in order to gaina better understanding• Noticing themselves achieving new understandings through “A-ha” or “Wow!”moments and they are interested in sharing these with others• Knowing their own strengths and weaknesses• Persisting in their learning instead of giving up and declaring “I don’t know howto”
Five Main Indicators for ResilienceGrowth mindset – after building a complex robot first that wouldn’t stay together, Hopedecided to rethink her construction and designed a simpler model.
Meta-cognition – during reflections of the maths learning a student wrote on a post-it notethat they could figure out where to place numbers on a number line between 0 and 1 but couldn’tgo past one. They identified that they would have to explore this tomorrow, highlighting differentways that they could do this.Student responses during reflection to describe what they did or didn’tunderstand and how they worked.
Adaptability – understanding that mathematics is interrelated and that knowledge in one areais useful and required in another.When sorting Hope first arranged her bears incolour groups only. She reflected on this andrearranged her bears in sub-groups according tosize as well as colour. This broke the bears intosmaller groups, which made is possible to estimateat a glance the group that had more.When sorting ,Cayleb first arranged his blocks inrandom order and found it difficult to tell which wasthe largest amount. He reflected on this andrearranged his blocks in ascending order and foundit easier to determine the size of the groupings. Weoften use the terminology “have I seen somethinglike this before? What worked and what didn’twork?”
Interpersonal – Developing and valuing working relationships with their peers. Whenproblem solving students are encouraged to seek the help of their peers and work alongsidedifferent people in group situations rather than independently. Majority of students thrive in thesegroupings due to their conversations about learning and working problems out together.“Uh oh” moment. Alexander realisedthat Fadia wasn’t counting one toone. He suggested that she ‘make aline’ so that her amount of fencescould match his.Resilience strategies: Trying anotheridea, teaching someone else.
Sense of purpose – Before learning about fractions, decimals and percentagesstudents brainstormed and gathered information about where we use these in our lives andcontinued to add to their ideas as they came across examples. Students had to create a planof a robot for their partner to construct. Their plans had to be informative and descriptiveenough for their friend to understand.Fractions, decimals andpercents brainstormPicture of a house
How the classroom supports this• Discovering new information for themselves that are connected to reality• Problem solving situations• Primary Years: Students are allowed the opportunity to decide whichprocesses they will take, what materials they will use, where they will workand with who, how they will record and explain their discoveries.• Junior Primary Years: Open ended process where students have a choice ofmaterials but the possible strategies are modelled and students are guidedthrough their problem solving. The language is explicitly used and taughtthroughout the thinking process.• Results are not the key focus, rather than the process taken. Reflections arefocused on not necessarily their ‘answers’ but the strategies they used,obstacles they faced and overcame and what they could try next time.• Mathematical discoveries are celebrated daily and students are experiencingfun while learning. They are given the opportunity to be mathematical,without worrying whether or not their answers are correct.• Strategies are explicitly spoken about and other people’s ways of working outare considered and shared and at times even copied.
Language for ResilienceResilient strategies used when problem solvingKeep tryingAsk a questionWork with a friendTry all ideasMake a modelUse concrete materialsBreak it into smaller partsDraw a picture or a graphHave I seen something like this before?Guess and check answerMake a listWOW! or Ah-Ha! moment
Feeling pride in their discoveries andlearning...celebrating theirachievements
Student videoWhat resilient indicators can you see? Whatstrategies has the student used when problemsolving?