The goal of this four part blog series is to consider the following questions:
- What is it about the way we talk about mathematics that promotes the acceptance of "I can't do that"?
- What might we do to shift the conversation?
Teachers’ own anxiety with teaching mathematics can have an adverse effect on students’ comfort with learning mathematics (Barack, 2018; Willingham, 2019). Ramirez et al. (2018) show that students in classrooms with math-anxious teachers perform at lower rates than those in classrooms where teachers are more confident with mathematics; these students also tend to demonstrate avoidance behaviours and fixed mindsets when it comes to learning subject area content. This evidence becomes further disconcerting when it relates to girls, as Bielock et al. (2010) highlight the correlation between female teachers’ math anxiety and female students’ ability, beliefs and achievement. Moving forward, it is suggested by Harper and Daane (2012) that as teachers become aware of their own levels of math anxiety, they are better able to learn how to prevent the unintentional bias of negativity toward mathematics.
Responding to Our Colleagues
It is at this point that I extend a challenge: if a colleague suggests, “I am not a math person” or “I am not good at math”, please do not let it go unattended. Instead, invite them to tell you more, tell you why, and offer your support to learn with them to enhance their positivity toward mathematics for the sake of our students. We have been taught to tackle illiteracy and to not turn a blind eye to behaviour: may we begin to wholeheartedly address innumeracy by asking, “How can I help?”.
How We Might Support Our Colleagues
Perhaps it is simply a case of helping them to see that they are often subconsciously engaged in mathematics and numeracy. It can start with a simple question: aside from teaching mathematics, how many times a day do you do or think about things mathematically? This can lead to conversation that may identify a variety of scenarios where one did not think they were engaging in mathematics (e.g. planning out time in the day, grocery shopping with a budget in mind), but they come to a realization that they were doing so - perhaps even with confidence!
Reassurance may come in realizing that we are not alone in this endeavour. Much in the same way that there is acceptance of the notion we are all teachers of literacy, we can continue to stress, as well, that we are all teachers of numeracy. Alberta Education (2021) states that “numeracy development is a shared responsibility of all subject areas.” It may be pertinent to engage teachers with their curriculum: where are mathematics and numeracy involved in teaching? It may come as a surprise to some to realize that timelines in social studies consider magnitudes of numbers as spans of events are identified or that calendar time includes concepts of patterns as well as measurement.
“Within the subject areas, students use numeracy to:
- understand and use small and large numbers
- interpret or represent information in graphs and charts
- understand and manage time
- visualize how objects are positioned within a space
- estimate distances” (Alberta Education, 2021).
Diving deeper into the numeracy progressions (Alberta Education, n.d.) may afford ways to illustrate spatial and quantitative information beyond simply mathematics teaching and learning, which may lead to increased conviction in their own instructional practice. Delving in the competencies in mathematics (Alberta Education, n.d.) as educators may provide opportunity to identify cross-curricular connections whereby planning for students to engage in numeracy activities might lead to deeper understanding, thus enhancing their confidence and improving their achievement.
The Language of Mathematics
When working with colleagues from the perspective of a mathematics educator, empathy may play a role in building teacher capacity. Anxiety in mathematics may stem from feeling as though it is a foreign language (Kenney et al., 2005) . Helmenstine (2019) honours this feeling by identifying that mathematics does have its own written vocabulary, grammar, and syntax. Burnett (2021) and Lappan (2000) speak to the need for carefully crafted lessons so that students can understand both the language of mathematics and how to leverage that language in context to understand and solve problems. This may present a formidable challenge for some teachers if they themselves do not have a grasp of the language of mathematics. Imagine trying to teach someone how to give directions in a language neither one of you understands - for some, this may feel like what mathematics teaching is like. Learning a language may come easier to some than others: thus the introduction of “rules” and “tricks” and “shortcuts” to help make sense of what is being expressed. However, such manipulations disguise the mathematics so that it may not be interpreted properly in contexts in which it is presented, thus limiting the ability to approach a problem for its solution. As we support our colleagues on their journey of overcoming their own math anxiety, may we honour math’s complexity as not being our first language, revel in the fact that it is a language of its own, and, where possible, translate for those who seek to understand that language in order to be understood.
Building Capacity: Self-Reflection and Professional Growth
In order to grow as an educator, one must realize there is a need to do so. As educators, in order to become aware of our own levels of competency (anxiety/confidence/skill/artistry) in teaching mathematics, we must first take time to reflect on our own practice. This will help us to identify the areas in which we seek professional growth as we build our own capacity. While a multitude of tools exist to support self-reflection, Pennant (2018) offers eight aspects to consider when reflecting on your classroom’s culture for mathematical problem solving and Merrit et al. (2010) pose eight dimensions as a framework for reflecting on mathematics teaching. Regardless of how self-reflection is conducted, it is not until we identify a need for learning that we can commit to fulfilling that need.
Building Capacity: Consulting
The role of consultant involves taking one’s own experience and expertise to an audience, whether it be one or many, and providing learning opportunities from which the audience leaves armed with more knowledge and understanding than when they entered. Much like direct teaching, this type of capacity building has its place as we seek to ensure a common understanding of mathematics, numeracy, and pedagogy. The consultant is often regarded as the expert with the means to make teachers successful. A consideration regarding this type of interaction is that it relies on the teacher having the efficacy to make changes in their own instructional practice with little support.
Building Capacity: Coaching
As a coach, typically one engages with a teacher, starting where they are at, and then moves on to identifying goals, creating a plan, considering possible obstacles to the plan and ways to overcome those obstacles, implementing the plan, reflecting on the plan, and continuing through the cycle over and over again. While expertise and experience in mathematics may be helpful in providing feedback to a colleague, it is more important to know how to elicit the goal, the plan, the obstances, and the reflection from the teacher as they take ownership of transforming their practice. Coaches empower teachers through the use of exploratory, open-ended, and invitational questions that begin with positive presuppositions about the teacher’s capacity. Considerations around coaching include that it is built on the premise that the teacher knows what they want to work on (and we know that we do not always know what we do not know) and that it requires multiple interactions.
Building Capacity: Community of Practice
Where educators can come together in a community of practice, they can work together to identify common areas for growth, share best practices, and learn cooperatively (Learning for All, 2016). From this perspective, mathematics educators join other educators as a way to cultivate learning together. The expertise in mathematics is varied in this case. The Ontario Ministry of Education (n.d.) shares thoughts when beginning to approach this type of capacity building for mathematics. Learning organized in this fashion, as instructional practice is enhanced, aims to shift culture as well. Considerations for communities of practice include that they function best when subscribed, not prescribed, and that they require multiple interactions.
Building Capacity: Collaborative Response
The simplexity of Collaborative Response is that it intentionally brings educational staff together with specific structures and processes for collaboration and student discussion that is informed by data and evidence while considering the supports that might be put in place to ensure student success. When it comes to mathematics and numeracy, Collaborative Response ensures time for teachers to collaboratively plan as well as to meet with other staff to share key issues regarding student learning and brainstorm supports to address those issues. This differentiation helps to grow the toolboxes of classroom teachers in providing universal instruction as well as differentiated supports in the classroom as all students are considered our students. Essentially, there is a shared responsibility for the success of each student, not only the ones in my class. As a teacher, I can be in a Collaborative Team Meeting to both inform about my own instructional practice (share my expertise) as well as become informed of the instructional practices of my colleagues (learn from others). Combined with layered teams to address students who need more intensive supports beyond the classroom, this mindset for supporting students is fortified by a framework that clearly articulates who is responsible for what and when. Considerations when building capacity through Collaborative Response include the need for ongoing, scheduled meeting times as well as it being a collective approach (it cannot be done in isolation).
Summing It Up
Forgive the math pun. :)
Research into mathematics teaching indicates there is anxiety among some educators that has the ability to negatively influence the success of students’ mathematics learning. Such a concern requires addressing. A lens of numeracy may encourage those who are math-anxious to recognize they do engage in mathematical thinking and thus build their confidence. In supporting our colleagues, we must recognize that there are different degrees of understanding the language of mathematics, and that that goal is to build capacity in instructional practice. While there are many approaches to building this capacity, the ones that have the greatest potential for professional growth are the ones where teachers engage actively. As we become more confident as teachers of mathematics, as teachers of numeracy, so will our students, and thus, we will begin to see sustained success.
Alberta Education. (2021). Numeracy in subject areas. Retrieved from https://education.alberta.ca/literacy-and-numeracy/numeracy-in-subject-areas/everyone/numeracy-in-subject-areas/
Alberta Education (n.d.) Competencies and current programs of study: Mathematics. https://education.alberta.ca/media/3576122/comp-in-math_20mar_17_final.pdf
Alberta Education. (n.d.). Numeracy progressions. Retrieved from https://education.alberta.ca/media/3402196/num-progressions.pdf
Barack, J. (2018). When teachers have a fear of math, their pupils can absorb the wrong lesson. https://www.k12dive.com/news/when-teachers-have-a-fear-of-math-their-pupils-can-absorb-the-wrong-lesson/518391/
Bielock, S., Gunderson, E.A., Ramirez, G. and Levine, S.C. (2010). Female teachers’ math anxiety affects girls’ math achievement. Retrieved from https://www.pnas.org/content/107/5/1860
Burnett, J. (2021). Make a change for good: Part 4. Retrieved from https://www.origoeducation.com/blog/mathematical-language/
Harper, N.W. and Daane, C.J. (2012). Causes and reduction of math anxiety in preservice elementary teachers. Retrieved from https://www.tandfonline.com/doi/abs/10.1080/01626620.1998.10462889
Helmestine, A.M. (2019). Why mathematics is a language. Retrieved from https://www.thoughtco.com/why-mathematics-is-a-language-4158142
Kenney, J.M., Hancewicz, E., Heuer, L., Metsisto, D. and Tuttle, C.L. (2005) Chapter 1: Mathematics as language. Literacy strategies for improving mathematics instruction. ASCD. Retrieved from http://www.ascd.org/publications/books/105137/chapters/Mathematics-as-Language.aspx
Lappan, G. (2000). The language of mathematics: The meaning and use of variable. Retrieved from https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Glenda-Lappan/The-Language-of-Mathematics_-The-Meaning-and-Use-of-Variable/
Learning for All (2016). What is a community of practice? Retrieved from http://www.communityofpractice.ca/background/what-is-a-community-of-practice/
Merritt, E.G., Rimm-Kaufmann, S.E. Berry III, R.Q., Walkowiak, T.A. and McCracken, E.R. (2010). A reflection framework for teaching math. Retrieved from https://www.researchgate.net/publication/258441120_A_reflection_framework_for_teaching_math
Ontario Ministry of Education. (n.d.) Capacity building series: Supporting numeracy. Retrieved from http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_SupportNumeracy.pdf