In this series, we will explore the eight research-based essential Mathematics Teaching Practices found in NCTM’s Principles to Actions. Today’s blog focuses on the first essential Mathematics Teaching Practices: establishing mathematics goals to focus learning.
2020 has brought many different challenges to teaching and learning across the globe. It has been fast. It has been sudden. It has been a first for an entire generation. Teaching has shifted from learning in schools to remote and distance learning from home. Despite this shift, we as educators are responsible for continuing to provide quality learning opportunities for our students.
Across the globe, whatever learning environment we face – online/remote learning or back in the classroom – two major questions remain:
- How do we support our students and teachers in this new world of education?
- How do we continue to support students when shifting from online/remote learning to face-to-face learning and then back to online learning at any given time?
For me, taking an evidence-based approach is an important first step. It brings to light what we know works and provides an important stepping-stone in supporting teachers with impactful teaching practices. In this series, we will explore the eight research-based essential Mathematics Teaching Practices found in NCTM’s Principles to Actions. Each blog will connect the recommendations from NCTM to the mathematics classroom and show how the evidence-based research supports online/remote and in-school learning environments.
Mathematics Teaching Practice #1 – Establishing mathematics goals to focus learning
Today’s blog focuses on the first of NCTM’s eight research-based essential Mathematics Teaching Practices: establishing mathematics goals to focus learning. NCTM believes that in order to achieve this, teachers and students carry out specific roles.
- Establish clear goals that articulate the mathematics that students are learning as a result of instruction in a lesson, over a series of lessons, or throughout a unit.
- Identify how the goals fit within a mathematics learning progression.
- Discuss and refer to the mathematical purpose and goal of a lesson during instruction to ensure that students understand how the current work contributes to their learning.
- Use the mathematics goals to guide lesson planning and reflection and make in the moment decisions during instruction.
- Engage in discussions of the mathematical purpose and goals related to their current work in the mathematical classroom. (ex. What are we learning? Why are we learning it?)
- Use the learning goals to stay focused on their progress in improving their understanding of mathematical content and proficiency in using mathematical practices.
- Connect their current work with the mathematics that they studied previously to understand where the mathematics is going.
- Assess and monitor their own understanding and progress toward accomplishing the mathematics learning goals.
Research Behind Goal Setting
In my last blog, I discussed the impact of Professor John Hattie's extensive meta-analysis of thousands of research findings and how this can be used and interpreted within a school context. One area of research that Professor Hattie demonstrates is essential in all teaching settings is goal setting, which he notes has an effect size of 0.56 (0.4 being a year’s worth of growth for a year’s worth of schooling).
Professor Christine Rubie-Davies from the University of Auckland has studied the importance of high expectations and goal setting and the positive impact they have when done in an effective way for students. She believes that all students must be given difficult, yet achievable learning goals to be motivated. The importance of establishing challenging goals rather than 'do your best' goals – whether online or in the classroom – cannot be underestimated. By setting challenging goals, the teacher develops and maintains a culture of high expectations.
How can teachers effectively set learning goals that challenge all students?
Learning Intentions and Success Criteria
Lessons need to include clear learning intentions with goals that clarify what success looks like. They should explain what students need to understand and what they should be able to do. This helps teachers plan learning activities and helps students understand what is required. Professor John Hattie’s research shows that having clear learning intentions and success criteria also help students track their own progress and more easily identify where they may need additional support to succeed. When teachers set and communicate clear lesson goals to help students understand the success criteria, students know where they are, where they need to go and how they are going to get there.
You can find examples of Learning Intentions (also known as Learning Targets) and Success Criteria in the Big Ideas Math series. These align to the learning in the series and teaching notes and provide teachers with a great starting point in setting goals and creating clarity when teaching and learning mathematics. Hattie (2012) believes that the key to setting learning goals and providing success criteria is to help students commit to the learning and provide the appropriate mix of success and challenge. Furthermore, by explaining the connections between learning goals, learning activities, and assessment tasks, teachers demonstrate the purpose of classroom tasks, making the learning visible to students. This helps students become self-motivated to use learning goals to monitor their learning progress.
Students feel supported when teachers help break their larger goals down into small, achievable steps that they can work through and evaluate each step throughout the year. Hattie (2012) believes that self-evaluation is considered one of the key benefits of ‘Goal Setting’ as a strategy because it encourages students to provide the evidence that they think demonstrates how they achieved their goals, while also recognizing the areas in which they need to improve.
In order for students to be actively involved in the process, the learning intentions and success criteria need to be visible at all times so that both the students and teachers can refer to them throughout each lesson. Learning goals should also be achievable for students of varying abilities and characteristics. However, this does not mean that students will have different learning intentions and success criteria.
The value of learning goals extends beyond a checklist of content/skills covered. They provide students with a focus and a chance to receive feedback which is a powerful force in improving student outcomes. Feedback can occur in assessing the learning goal at the start and end of the lesson. This encourages students to take control of their learning and engages them in meta-cognitive processes (Hattie, 2012).
Assessment must be authentic to provide teachers with evidence of prior learning, and the information they need to set goals that offer each student the appropriate level of challenge. Assessment tasks must be appropriate for each student as she/he demonstrates knowledge and skills at many different levels. Using a framework such as the SOLO Taxonomy, Bloom’s Taxonomy, or Depth of Knowledge (DOK) ensures that tasks include lower and higher order understanding, skills, and knowledge at different levels.
In the unknown world of teaching and learning in 2020, one thing is for sure: goal setting can be used in all environments and is an essential tool for teachers to provide students with support to let them know where they are in their learning, where they need to go, and how they are going to get there.
When setting mathematics learning goals, keep these tips in mind:
- When teachers use goal setting as a strategy, students can self-monitor their progress and take ownership of their learning when they have clear learning goals to work towards.
- Clear goals and small steps toward larger goals provide evidence to both the students and teachers that they need to continue to demonstrate that they achieved their goals, understand any misconceptions, and work together toward the learning goal.
- When students understand their goals and know how to work towards their goals, they can make greater connections not only with the learning goals, but with the learning activities and assessment tasks.
- Learning goals can actively engage students in identifying strengths and areas for improvement of their own learning to frame future learning goals, understandings, and aspirations.
We will continue to share with you practical examples and connections to the NCTM evidence-based Mathematics Teaching Strategies that will impact all classroom environments. Stay safe and well. Remember, you are doing a great job! Keep in touch, ask any questions or comment via twitter (@_sophie_murphy_) and through Big Ideas Learning and National Geographic Learning. I look forward to connecting with you all again soon.
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. Routledge, NY.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
Rubie-Davies C, Hattie J, Hamilton R. Expecting the best for students: teacher expectations and academic outcomes. The British Journal of Educational Psychology. 2006 Sep:429-444