Rachel McCann | November 19, 2020
Differentiating Maths Like Never Before
When I was completing my Masters in Special Education I was given the task of adapting an area of the primary curriculum to cater for gifted and talented students in a unique way. While other students used De Bono’s Thinking Hats to unpack literary texts or constructed project matrices to allow selection of activities based on areas of talent and preferred learning styles I wanted to embrace the “in a unique way” part of the brief. I wanted to create a teaching program which no other teacher had yet created. So I decided to create a full year’s teaching program combining Benjamin Blooms Taxonomy and the Mathematics syllabus for Grades 2 and 5.
In its very first conceptual state Bloomsmath, as it has since been dubbed, was a complex multiple paged spreadsheet of 6 hierarchically more cognitively complex activities for each of the 16 areas of the mathematics syllabus for Years 2 and 5.
Based on the 1956 work of Benjamin Bloom and his colleagues, Bloom’s Taxonomy is a framework for categorizing educational goals into six categories: Knowledge, Comprehension, Application, Analysis, Synthesis and Evaluation. The 6 categories are sequentially more complex and competence in each area is a prerequisite for moving onto the next skill or ability level. While each category contains subcategories, all lying along a continuum from simple to complex and concrete to abstract, it is these 6 main categories that are most commonly used. A new, revised version of the taxonomy was released in 2001 but I chose to use the original categories as I felt students need to ‘know’ and ‘comprehend’ Mathematics rather than just remember it.
When I presented my original ‘project’ it was positively received and in fact so positively received that I was asked to present at a conference on differentiation held in Sydney. The following year I wrote the missing programs for Years K to 8 and presented again at the same conference the following year. I then spent a number of years working with schools to implement this program in their schools before leaving teaching for a couple of years to raise my children.
During this time I was able to reflect on the Bloomsmath programs and the fact that I was unable to get to every school who wanted to implement them. I also realised that teachers were time poor and did not have the time to unpack the complex matrix for their class so I decided to take these lesson and turn them into activity sheets so any classroom teacher would be able to implement this program with their class.
With almost 100 pages of activities for each grade the new version of the program is designed to allow teachers to work with the students who are struggling to achieve the knowledge level while capable students can progress through the more complex levels at their own pace. It is also designed to ensure all students, regardless of the level to which they progress, are exposed to the metalanguage of mathematics and are provided with challenging questions to encourage higher order thinking about each mathematics concept.
What Bloomsmath does is ensure students are working within their grade specific outcome towards true mastery. They are given a chance to analyse and synthesis mathematically so they are stretched longitudinally within an outcome rather than merely glossing the surface of it before being exposed to more advanced concepts from the next grade level. By reinforcing the building blocks of mathematics students have the scaffolding required to truly enjoy mathematics and delve into the complex possibilities each syllabus topic provides rather than merely completing endless worksheets of questions.
Many of the activities involve students working together, playing games that challenge and reinforce topics and can last multiple mathematics lessons. Students may achieve higher levels in some curriculum areas than others, may continue to struggle with the knowledge activity and require intensive support to master every basic concept or may complete all the activities for every level although I do not think there is sufficient time in a school year for this to happen in every area of the curriculum.
What will happen though is every student will be working to their optimum level and will be working with students at their same level. All students will be exposed to higher order thinking in mathematics and will be challenged to think about mathematics not just compute with mathematics.
When Bloomsmath is implement successfully students will enjoy mathematics as they will feel challenged yet supported in their learning. They will enter every mathematics lesson knowing that they will enjoy their lesson without the risk of boredom or the frustration of being pushed too far out of their comfort zone too quickly. Their learning will be supported and enriched and differentiated to their exact level which was exactly what the original design brief asked for, it just took a few years to get all of it compiled.
You can find the new worksheet versions of Levels 1 to 6 for Grades K to 5 on the Bloomsmath section of the website with Level 5 going live this week. The final set of original design brief asked for, it just took a few years to get all of it compiled. You can find the new worksheet versions of Levels 1 to 6 for Grades K to 5 on the Bloomsmath section of the website with Level 5 going live this week. The final set of sheets for Level 7 / Year 6 should be finished before the start of next year. I will of course let everyone know as soon as they are done.