Mathematics Consolidation – Year 6
Fractions, Decimals and Percentages
During Term 3, three lessons a week, I worked with a small group of Year 6 students who required further development in their knowledge, understanding and skills in working with fractions, decimals and percentages. I implemented many of the teaching strategies that I had gathered during the Number sense professional development day to broaden my professional knowledge and teaching practice. (7.4)
Prior to beginning the group work, I made contact with parents/carers via a letter to communicate the purpose of the work and to their gain permission to work with their child. (3.7), (7.2), (7.3)
Additional maths support letter to parents.
To diagnostically assess student’s current point in learning, I drew on knowledge of student’s prior summative assessments and reports. I mapped content to curriculum requirements to design learning sequences and lesson plans. (2.3) This allowed me to plan lesson sequences using knowledge of student learning, content and effective teaching strategies. (3.2) Knowing that small group work improves student learning outcomes (Fuchs, D,. Fuchs, L., Powell, Seethaler, Cirino, & Fletcher, 2008).
This overview spans 8 weeks, leaving space in week 9 and 10 if concepts took longer to teach. I was aware that being taken out of class to do more mathematics, could make students feel inadequate against their peers who were staying class to do ‘normal’ maths lessons (1.1). One of the strategies I used to counteract this was to use positive psychology (Seligman, 2011) and growth mindset strategies (Dweck, 2005). I focused on students’ strengths. We explored how the students were already powerful mathematicians and that they use mathematics every day. Sometimes we take this fact for granted. For example, students realised that when they pack their lunch box, they use their spatial awareness, measurement and geometry skills. (3.7) We acknowledged that we do this without recognising that we are using our mathematics skills. I explained that people are born with a mathematical brain (Simon, Hespos, & Rochat, 1995; Schneider, Bjorklund, Damon, Kuhn, & Siegler, 1998). I explained that everyone can learn mathematics, it is just that we all learn it at different rates and in different ways. (1.2) My intention was to teach the students to be positive about their mathematical learning and to use a growth mindset (Dweck, 1999). I called these students powerful mathematical learners. Initially we looked at key mathematical language to assist their learning. For example, the base ten system.
I provided clear learning goals and scaffolded tasks. I organised and selected content into an effective learning and teaching sequence, beginning with fractions. I interweaved fraction, decimal and percentage concepts throughout the learning tasks. Finally teaching decimals and percentages. (2.2), (2.1)
I incorporated fun, hands on, concrete tasks, warmups, card sorts, graphic organisers and visual aids. (2.5) Some of the concrete tasks included, which doesn’t belong, smarties sort and maths concept sorts. I used white boards for each student and incorporated warmups and reflections in each lesson. I attempted to make the learning fun, meaningful, interesting, challenging and engaging. (3.3), (2.2)
The students had their timetables and calculators on hand to reduce cognitive load which assisted these students who had cognitive working memory issues (1.2). The use of concrete tasks, moving to more abstract as the term progressed assisted student understanding of the mathematics learning objectives (Moon, 1999). (2.1) This allowed me to the support learning and full participation the students in the group who had Autism and ADHD. (3.1)
Throughout the teaching and learning I formatively and summatively assessed student work. Further to the formal assessment strategies used, I informally assessed students in each lesson via observation, discussion and marked student work. This allowed me to continuously adjust how I was teaching the mathematics concepts and content to enhance student learning growth. For example, if I could go over concepts, break down tasks or give the students more concrete examples. (5.1), (3.1)
During this project, I continuously reflected on what strategies were working to engage students and enhance their knowledge and understanding. At one point I was using questions directly from the Year 6 mathematics textbook. I quickly realised that these were not effective. Therefore, I began to adjust and make up my own questions and activities that were based on the concepts from the same textbook. This resulted in improved student learning, which was reflected in formative assessed tasks and summative test scores as the project progressed. (3.6), (3.2)
At the end of the term I reported test scores to students by showing them the graph as shown below (asking permission from all students, as they could see other student’s scores). They loved seeing their growth in learning in this way and we celebrated their success by sharing out smarties (equally) amongst the group at the end of the term. This graph demonstrates one way that I can record and report student learning data. I entered the data into an excel spreadsheet prior to creating the graph. This allowed me to keep accurate and reliable records of student achievement. (5.5)
We finished with one lesson to spare in week 10. We did some revision and had a celebration due to the amount of learning growth the students made. The impact from this project was that my mathematical teaching and numeracy teaching skills have improved. Further, the students made significant growth in their mathematical learning. I printed off each students individual achievement to share with parents. (3.7), (7.3) Therefore, in Term 4, my mentor teacher would like me to work with and extend a higher end group of Year 7 students in her class.
This resulted in a significant growth in these student’s learning and summative test scores. Click here to see enlarge student pre and post summative assessment test scores.
Therefore, in Term 4, my mentor teacher would like me to work with and extend the higher end group of Year 7 students in her class.