How do I start spiraling my math curriculum?
Change can be seemingly overwhelming and it can be difficult to know where to begin. It is important to remember to always start small. "Large scale reform creates the danger of asking teachers to abandon their experience and knowledge, which is not a good starting point for teacher buy-in and teacher professional growth" (Gadanidis et al., 2016, p. 238). Educators put a great deal of time and effort into the development of their programs, so we are naturally hesitant to scrap what we have been doing, especially as there are pieces of it that we find to work exceptionally well. Gadanidis et al. (2016) respond to this concern with the suggestion to focus on curriculum covering and flexible implementation (i.e., one big idea at a time). To give spiraling a fair shot at success for your students, you must set yourself up for success first. This means taking your time to first understand why you are making this change. Then, it means setting reasonable goals and expectations for implementation, keeping in mind that math is likely not the only subject you are responsible for planning and teaching.
SET-UP AND MATERIALS
WHAT KNOWLEDGE DOES THE TEACHER NEED?
Before considering the knowledge that would be required for the teacher, let us take a moment to discuss the best options to inform and educate teachers on spiraling. Darling-Hammond and Richardson (2009) suggest that in order for professional development to be “sustained, coherent and intense” (p. 2), a minimum of 14 hours is required. Darling-Hammond and Richardson (2009) also suggest that teachers work together in grade teams and be given common prep time and the observation to observe each others’ practice. As professional development is tied to available funding, the 2016 Ontario Renewed Math Strategy policy was created to offer supports such as professional learning for teachers and principals, the development of math lead teachers, and online access to math resources. While the policy states its goal as “to help students gain the math knowledge and skills they will need for the future”, further details in the policy, such as available and increased support to schools, acknowledges the relationship between teacher preparedness and student success.
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When providing teachers with professional development, it is important to have the teachers experience new ways of teaching prior to implementing new strategies (Dorier and Maass, 2014). Ideally, teachers would be involved in professional development that allows them to engage in a lesson as the ‘students.’ Alternatively, teachers could be provided with release time to watch another educator lead a lesson and observe the new teaching strategy in action. Not only does this help with understanding and implementation, but it also increases teacher engagement and buy-in (Davis and Simmt, 2006)
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“Not only do teachers have to be familiar with the subject matter, they must be confident enough to recognize and generate equivalent interpretations without aid” (Kajander et al., 2010, p. 51). There is a misunderstanding that teachers need to have a higher level of mathematical knowledge; in actuality, it is not about math teachers needing to know a higher level of math, but a “knowledge of how mathematics topics are connected, how ideas anticipate others, what constitutes a valid argument, and so on” (Davis and Simmt, 2006, p. 295). In the case of spiraling, teachers must develop a deep understanding of the curriculum expectations and begin to identify connections between curriculum expectations.
Teachers are more empowered to make and maintain changes to their program delivery if they experience success (Lannin and Chval, 2013). Hence, it is of the utmost importance to set-up teachers (and classrooms) for initial success so that they will be more likely to continue and benefit from further success.
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Gibbs (2014) suggests that teachers could better implement a spiral curriculum by setting specific goals for the school year or semester and then “teachers would scaffold the instruction as necessary for success and then descaffold it as needed” (p. 43). This type of compressed spiral curriculum allows students to receive the support necessary and provides the teacher with the opportunity to challenge the students appropriately. Thus, an initial aspect to set-up would be the creation of specific goals for learning through consultation with the curriculum document. It is imperative that educators derive goals from their curriculum when planning as this is the mandated set of expectations. Phillips (n.d.) discusses the need for teachers to sit down with their curriculum and notice the connections between concepts. This can be daunting, but the benefit is that students should be more likely to demonstrate understanding by repetitive practice over time and teachers are not focused on a unit ending, but rather assessing a skill all year – giving the student more time to show the teacher they are capable. The recommendation of Gibbs (2014) to scaffold and descaffold allows teachers the ability to differentiate instruction for students. The creation of diagnostic and formative assessments will be a necessary piece to spiraling the curriculum as it will help the teacher to identify the types of scaffolding required by his or her class.
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I have spent a great deal of time discussing the importance of having a deep understanding of your curriculum and truly that is a very important piece to setting up for spiraling. There are however, other aspects to set-up. Being that this is not a change in curriculum expectations or teaching strategies, but rather a change to the order of concepts taught, there is no need to alter the materials available in the classroom. Teachers would continue to teach using manipulatives of their choosing.
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There are a number of resources available to math teachers and some may be repurposed to work within a spiraled classroom; however, there are also a number of resources becoming available that are already geared towards a spiraled learning environment. See the Available Resources section for more information. Given that spiraling the curriculum is more about a reordering of content, teachers may find that they can use previously created portions of lessons and unit plans in alignment with their new spiraled plans.
AVAILABLE RESOURCES
The following table has been created to provide an overview of some of the available resources for spiraling the math curriculum. Click on the name of the resource to link to the actual website, or click on 'Details' for a description of the resource along with a list of some pros and cons for that particular resource. Please keep in mind that there are a number of Facebook groups and other learning groups appearing over social networking that can help provide you with support, encouragement, and resources. This can be invaluable, especially if there are not many individuals at your school that are engaging in this same process.
Start-Up Guide
Gibbs (2014) references the work of Jerome Bruner stating, “Bruner was right but his scale was wrong. His conception of spiral curriculum delivery is accurate from a broad perspective, but its implementation needs to be more compressed. It can be and is much more powerful when scaled down to fit the individual classroom or grade level” (p.44). Following a framework built off of the work of Bruner, but allowing for the reconfiguration of Gibbs, Gibbs (2014) offers that “this way not only allows students and teachers to witness powerful change over time but, in fact, is much closer to Bruner’s intent that learning is connected, builds upon itself, and grows” (p. 44). All of this is to say, once again, that one of the most important things a teacher can do to successfully spiral their mathematics program is to have a firm grasp on his or her curriculum. Pearce (2018) provides his own six step start-up in the second video of his spiraling series, and I will provide my own below:
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1) Know why you are doing this. Do not spiral your curriculum just because it sounds cool and you heard other people are doing it. Go to the Why page of this website and get an overview of the research, reasoning and benefits. Being able to explain why you are doing this will not only make you better able to evaluate your success, but it will also make you more confident when speaking with your colleagues, administrators, students and parents. Education is a team effort and parents in particular will want to know why this is best for their child. You will want to be well-versed in the reasons why you made this programming decision and help everyone to understand why this is the best way to improve math learning in your classroom.
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2) Read your curriculum. Then re-read it. Then read it again, this time looking for overall themes or connections (a.k.a. ‘Big Ideas’) that you could use for your spirals. As mentioned by Pearce (2018), this is something that is easier done when you have been teaching a grade for awhile and are more familiar with the curriculum content, but is sound pedagogical practice for a teacher at any point, regardless if they are new to the grade or a veteran.
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3) Create a visual representation of each spiral. This could be done digitally or just on regular paper. The point here is to label each spiral with the major concept it addresses and then list the expectations that you will be teaching through this spiral. It may help to colour-code each strand, as Ontario teachers are still expected to assess each strand individually for report cards. Do not worry about the order in which you will address expectations just yet. This is a work in progress. Instead, come up with 2-3 overall learning goals for each spiral that encompasses the curriculum expectations.
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4) Determine an order for teaching your spirals. Keep in mind that spiraling means coming back to concepts repeatedly over the course of the year, not to reteach the same thing, but to delve deeper into the learning of that content (Penney and Walker, 2019). You are going to want to ensure that you are listing spirals more than once. It should be evident which spirals will require more time/visits than others based off of the number of expectations listed within it and be the magnitude of the concept involved. Be sure to use your school-year as a timeline for this ordering so that you are keeping in mind the time frame you have to address your curriculum.
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5) Create mini-spirals. Order the expectations within each spiral to help divide them into the mini-spirals you created in your long-range plans from Step 3. Do not be tempted to sort expectations by strand. That defeats the purpose of finding overall themes/concepts. Instead, look for connections across strands. If you are teaching multiplication of whole numbers can you also be teaching how to calculate the area of a rectangle?
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6) Access your resources. You now have a plan for how the year will progress, so it is time to start planning your lessons. Given that you have been keeping curriculum expectations in mind, you can access lesson plans or activities from EduGAINS, Tap Into Teen Minds, and MathUP by searching for the correct topic. You can also open your own files and reorganize your lessons to match your new delivery plan.
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7) Assess everyday. Yes, you read that correctly, every day. I am not talking about traditional tests or quizzes, but rather formative assessments such as checklists and observations. While assessing this frequently may seem like a lot, it will actually be way less intensive and you will find yourself far more aware of what individual students can and cannot do. This will be invaluable for identifying students requiring additional small-group instruction and for knowing when your students are ready to be challenged or move on to a new concept.
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8) Connect all learning. Move away from the idea of assessing a unit and then moving on to something new. Help your students become comfortable with the idea that anything that they learned yesterday, or last week, or last month could be brought up again tomorrow. Delayed assessment is a much better indicator of understanding than a test immediately following a unit (Penney & Walker, 2019). This is because the latter is usually accompanied by a review day and a list of expectations encouraging students to ‘cram’, while the former is telling students that the learning is important beyond any unit time-constraints.
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9) Celebrate your wins and learn from your losses. Celebrate each and every win, from the big to the small. See if you can determine what led to that success so that you can apply it to areas where you feel like you are losing. Keep in mind that change rarely goes smoothly, but if you stick it out long enough, you can reap the benefits on the other side. Be prepared for things to go wrong and for having to scrap lessons and rework spirals. Teaching is the art of being flexible. This is to be expected and not an indicator of failure.
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10) Cut yourself some slack. Rome was not built in a day. This is likely not the only class you are teaching. You probably have a life outside of work as well. All of this is to say, be mindful of your well-being. This is a lot of work and it will not happen overnight. This is something you will tweak and adjust for years to come, so do not be afraid to go to bed at a decent hour and have some lessons that are ‘good enough for now’. As long as you are always striving to improve and always sticking to your curriculum, you (and your students!) will be fine. This is not about perfect. This is about recognizing there is a better way and doing the best that you can at the moment to make these changes a reality. Do what works for you, your family, and your mental, physical and emotional health. You can only do what you can do.
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I sincerely hope that this website has provided you with the information and resources to spiral your math classroom. Please see the About Me page for more information about me and how you can contact me to let me know how spiraling is working for you!