Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts By Jo Boaler

Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts by Jo Boaler (2015)

Found a few years ago during my ALiM work, I keep referring back to this article and  https://www.youcubed.org/ website. This work is about developing number sense instead of memorization of facts, it unpacks the idea of learning math facts along with a deep understanding of numbers and the ways they relate to each other.

In a critical research project, researchers studied students as they solved number problems (Gray & Tall, 1994). The researchers concluded that low achievers are often low achievers not because they know less but because they don’t use numbers flexibly – they have been set on the wrong path, often from an early age, of trying to memorize methods instead of interacting with numbers flexibly (Boaler, 2009). 

Based on my experience, some teachers want their students to drill in basic facts and times tables as this is 'a good old school that worked well in the past'. Saying that we don't really have any research data to support this statement. I remember a lot of my classmates who hated maths because they didn't understand it or had to sit timed tests. I was one of them and I didn't enjoy that 'good old school' approach. 

I believe that the current decline in student achievement in maths is caused by a lack of maintenance or an unbalanced or inconsistent maths programme. 

• Do we all have a solid maths block every day four or five times a week? 
• Do our students practise and apply the knowledge and concepts taught in class or just do some busy work during their independent activities? 
• How can they develop fluency without mileage and purposefully created and provided opportunities? 

According to the NZC,  'number' should be the focus of 60–80 percent of mathematics teaching time during the first four years at school and 50-70 percent afterwards. 

Here comes a common misunderstanding or misconception. The curriculum requires a lot of time teaching 'number', but modern research talks about reasoning. The answer is simple. The 'old school' is about memorizing facts while the modern school is about developing fluency through making sense and connections, and talking about reasons for the use of different methods. Students need to learn to calculate through number sense, as well as spend time on problem-solving and reasoning. 

One of the great methods for teaching number sense and math facts at the same time is a teaching strategy called ‘number talks’ that many of us have been implementing already. Research tells us that the best mathematics classrooms are those in which students learn number facts and number sense through engaging activities that focus on mathematical understanding rather than rote memorization. (Jo Boaler)

At the end of her article, Jo compiled some great and engaging activities that can be used in any classroom to support your tamariki number sense development. 

Hybrid Learning - Creating Inspirational Learning Environments

This year educators faced a number of challenges, including students' poor attendance due to covid, low academic levels of some students as a result of their inconsistent approach to learning during lockdowns,  and general issues with re-engaging when they are back at school.

First, I decided to focus on making learning fun, engaging and inspirational to my team: both students and team members. My perception of the initial step in forming my inquiry was in line with Russell's question: 'How do I have present, happy, healthy and engaged tauira (both students and teachers) who are learning in the Goldilocks Zone?'

I believe that you’ve already heard about the Goldilocks Zone but think it's still worth clarifying its definition. Theo Dawson: 'It’s the range in which a learning task is just challenging enough to support optimal learning by stimulating interest and triggering the dopamine-opioid cycle—the brain’s natural motivational cycle. The brains of babies and young children are wired to learn in the Goldilocks Zone, but formal education often disrupts the dopamine-opioid cycle. As a consequence, many (perhaps most) older children, adolescents, and adults must rediscover the Goldilocks Zone if they want to learn optimally from everyday experience.' 

So, we needed some fun to improve our tamariki learning experiences, hook them up and motivate them to be present and engaged. Magic and collaboration formed my response to the situation: as a team, we dived into the world of magical learning and teaching. We’ve been busy designing our magic wands, using them and sharing our creative stories. It looks like we managed to sprinkle some magic over other students as this definitely improved their attendance and engagement.

The results were rewarding:

• students' engagement was very high - including the students who worked from home and participated in our activities via Google meets.
• improved reading and writing outcomes
• creating a positive and collaborative learning environment
• improving and taking my team's collaboration (teachers) to the next level
• increased attendance!

How to Raise Student Achievement? Q+A episode

I really enjoyed watching last Sunday’s Q + A, from TVNZ on Demand, https://www.tvnz.co.nz/shows/q-and-a/episodes/s2021-e11  as earlier this year I posed the same question for my own inquiry. Although I focus on developing critical thinking and cognitive engagement across the curriculum, my biggest focus this year is on Maths.

It was very interesting to listen to different points of view and confirm my own understanding of current problems in maths teaching in NZ. I think I am lucky enough because I have insight into different international educational systems as I came from the European part of Russia, and I'm also familiar with other European educational systems.

I truly believe that some NZ teachers don't have enough content knowledge in maths. Some of my colleagues don't feel comfortable teaching maths as they are not 'fluent' in it.  Some classes don't have a structured programme because teachers don't really understand maths progressions and pedagogy. I observed lessons when students were asked to solve equations and they struggled to do so simply because the numbers were abstract to them, those students had to use material instead. 

I agree with Prof Bobby Hunter who emphasised the importance of a balanced programme (direct instructions, practice and problem-solving (=create part). A few years ago, we went through a maths PLD that promoted problem-solving. It was very confusing as the kids had to solve problems using various strategies and we were supposed to discuss those strategies in a group. The explicit teaching and scaffolding were missing and I questioned that. However, that PLD introduced the Talk Moves that I implement in all subject areas.

Since that moment, I reflected on my previous international and NZ teaching and learning experiences, and decided to take the best parts that proved to be working well across all the subject areas: 

• direct teaching of new concepts, 
• practice - application of new learning
• use of materials, hands-on
• learning conversations (strategies, creativity in maths)
• problem-solving 
• acceleration vs filling gaps
• integrated learning - purpose!!!

My hypothesis is that designing a well-balanced purposeful classroom programme based on the above High-Leveraged practices will help develop my students' critical thinking and cognitive engagement and improve their outcomes in maths and other learning areas.

My Change of Practice Reflections and Tweaks

In this post, I'd like to collate evidence of my change of practice and explain my reflections and tweaks that I have been making during this bumpy year.

A brief summary of my improvement change in a few words: Learn-Create-Share, student interests and a real purpose behind this process! 

My Reflections and Tweaks: I created a new habit of regularly asking myself a number of questions and collecting evidence to support my conclusions: 

• How did the students respond to my new approach/strategy/ tool? 
• What are their learning outcomes after implementing my changes - evidence of improvement? 
• Are things better than when typical/traditional approaches/strategies/tools were used? 
• What could be done differently to secure further learning gains or consolidate existing ones? 

2020 has been a very interrupted year and I had to adapt my teaching approaches and tools to the new learning environment. I've noticed that instead of narrowing down my focus, I had to be flexible and very responsive to my learners' interests and needs, especially during remote learning times. I tried a number of activities and I must admit that some of them didn't really resonate with my young learners when the others hugely motivated them. The students continued to work on those tasks even during their holidays! 

My students were absolutely excited to 'be heard' - at some stage I noticed that they took ownership of their learning, initiated learning and participated in work that had meaning to them and others. My target group consists of 6 boys and 2 girls and this approach helped me to turn them into passionate learners. 

My tweak during lockdown - creating an online class community using blogging and commenting tools. It was explicitly modelled and taught during the first days in lockdown. Soon, my learners began to share their experiences through their blogs and other students gave them feedback. I think that introducing and fostering peer-feedback was a big win as my learners got a real audience and timely responses to their posts. At the same time, it was a great opportunity to reinforce cybersmart learning. I continued this during in-class developing into a new norm amongst our Y2/3 learners.

What worked really well and is supported by evidence:

• Blogging and commenting is not natural for some of the learners. How can we change this? Plan for it, allow time, motivate by purposeful and interesting tasks. Make their comments important! Create a culture of blogging and commenting. I believe that "Summer journey" is successful because of the feedback they get. 
• Optional topics/ choices for writing keeping in mind that the lesson's WALT had to be covered.
• Purposeful reading and writing tasks, e.g. creating their own games, trialling them, improving, presenting to other students to play. 
• Student-created Kahoot quizzes - real purpose to read to learn, create, proofread and edit for clarity and share with other students across the school!
• Implementing drama - my boys were enthusiastic and bursting with ideas, they did lots of reading and writing gave and received feedback, took risks, etc
• Use of word problem-solving in Maths provided extra opportunities to practise their reading and writing skills, deepen their thinking and comprehension, apply these skills to solve real problems. Use of Maths vocabulary.
• Effective questioning. I had to rethink my questions to make my learners think and understand topics deeper, make connections and, as a result, apply their new knowledge and skills to come up with a sophisticated answer.

These changes in my teaching resulted in student progress and improvement. Their engagement was easy to observe in-class, it was also video recorded (various class videos, online Google Meets, Manaiakalani Film Festival and other LCS projects)

End of Term 3 Data. As stated in the previous post, all my students have moved up their reading and writing levels despite two lockdowns and an interrupted in many other ways year.

Boys in Literacy - Professional Development with Marshall Diggs

If I was to summarise the key things I took away from this Professional Development what would they be and why?

Marshall's inspiring presentation was aiming to empower teachers to understand boys as learners and equip them with skills and strategies to enable boys to achieve and succeed in literacy and in their learning in general. As we know every child is different but boys do learn differently to girls, and it was great to listen to his ideas and reflect on my own practice. These are some of the points I found most interesting:

• Being CLEAR means being KIND to the boys
• Competition gets them excited
• Boys learn best with short and sharp exercises (active games, PE breaks, brain breaks, etc)
• Who are their male role models? Do they see men writing for fun?
• Are there spaces where boys like to learn?
• What topics do they prefer to read about? What will engage them?
• Be firm, fair and fun
• How much talking is happening in a lesson? More reading/writing, less talking (teacher talk)
• Relationships with our students is a priority
• Learning is more important than the result
• Align the curriculum with the child and put the child at the centre.

How has this professional development challenged my thinking?

I haven't changed my thinking, this PLD just confirmed that the use of the LCS pedagogy helps empower my male students to succeed in their learning. This year, I was impressed by the enthusiasm and engagement shown by the boys during our LCS projects. I'm very glad that I managed to involve more junior syndicate teachers in our LCS projects and see our boys' growing engagement and love of learning!

What aspects of my practice would I consider changing as a result of this professional development and why?

There are some pretty amazing things happening in our school but we can always be reflective and look at ways of improving. My plan is to have this conversation during our next team meeting and develop a plan to support our male learners:

• introduce short breaks and include them in our daily planning: 

- Word association game (president = Trump, Fruit = orange etc.)
- Give a fist pump to 4 people/elbow bump, touch 4 walls, find 4 green objects, etc
- Ninja punctuation activity: Capital letters - fist pump, Full stops - turn, Comma - twist,     Number - signal, Paragraph - yee hah
- Summary (in 3 words). Turn to your buddy and tell him/her what are you going to do this holiday? Then the buddy has to summarise in 3 words. Other students are to guess:-)
- Catch hand/finger game (activate both hemispheres of the brain - brain exercises)
- Word scrabble: how many words can you make from this one word (give time frame).

• Literacy - inspiring topics: Factual/ Competition/ Humour/ Survival/ Conflict/ Adventure
• Shared reading - big books - align with their interest and our LCS Term 4 plan
• S. Cameron and L.Dempsey activities
• LCS project - our learners have to be active participants
• Art - collect student voice! Differentiation.
• Maths - problem-solving and hands-on learning vs drilling
• Inclusiveness - identity and connections 
• Digital curriculum and digital tools to support boys' learning/ engagement

The Importance of Teacher and Peer Feedback during Remote Learning

I believe that we all know that giving feedback to students can be the bulk of the workload. Is the payoff worth the immense effort and time? In Visible Learning, John Hattie noted that feedback is “one of the most powerful influences on learning and achievement”, so if you’d like to increase student achievement in your classroom, feedback can be the key to making it happen.

Blog commenting is a great and powerful teaching and learning tool which cannot be disregarded. Reflecting on my own experience,  I believe that online feedback helped promote good communication and build stronger positive relationships within our Room 5's classroom community.  Blogging and commenting provides authentic experiences to purposefully utilize students' reading and writing skills. I always encourage my learners to check out their peers' blogs, give, receive and respond to feedback. 

My 2020 lockdown experiences proved that promoting peer blog commenting helps connect students with their friends, teachers and wider communities. Moreover, according to research, through exposure to a multitude of opinions and through awareness of writing for a wider audience, blogs also foster cognitive engagement and critical thinking because learners need to reflect on the possible reactions of others to their postings.

Examples of my Y2-3 learners' comments: 

Profiling: understanding the nature of my students’ learning strengths and needs in detail

There is a complex of factors that influence student's learning. Getting to know your students is extremely both for their well-being and academic achievements. 
The more we understand our students, the more efficient we can ensure their learning successes. When we have an in-depth understanding of how our students learn, there is a major impact on diagnosing student needs and planning effective programmes and supports. 

I combined the data gathered during in-class learning in Term 1 and the formative data collected during distance learning ('Covid-19 data'). 

During the lockdown, I experienced a new opportunity to look inside our learners' lives and observe them learning from home, observe their learning styles, reveal their personal interests, motivation and key competencies. Interestingly, I enjoyed a very high level of engagement in comparison to similar junior classes in my school. I believe that one of the factors that contributed to this success was a love of learning and self-motivation of my learners that we have been developing together during in-class learning.  Another factor was the use of personalised tasks that helped to keep my students engaged and motivated. Effective learning takes place when the amount of task structure by the teacher matches a student's level of development. 

My 2020 inquiry is about raising student achievement in literacy by promoting deep learning that requires students to develop cognitive engagement and critical thinking across the curriculum. I decided not to change my inquiry focus. After the lockdown and distance teaching I witnessed and confirmed for myself that understanding of learner identities is not just important but crucial for effective teaching and learning. 

Pre-Covid data: 
I analyzed results of the beginning of Term 1 Running record in reading and e-asttle in writing and found that most of my Year 2 students are well below the expected levels both in reading and writing. My year 3 students are placed at different levels, however, all of them require to focus on reading comprehension, vocabulary and spelling. 

I looked closely at the RR and identified that while my Year 2's need to work on decoding and comprehension skills, my Year 3's students mostly require to focus on making inferences and improving their evaluation skills.
The e-asttle writing data and their independent writing exemplars also suggested focusing on ideas, vocabulary and spelling.
All of these findings helped me to identify and prioritize 3 main areas for developing my teaching intervention: general knowledge, vocabulary(meaning and wordbuilding) and spelling (phonics, H-F and word building).

Formative "Covid-19 data".
Formative data collected during distance learning also showed that my students have limited general knowledge of various topics. Based on various reports from Reading eggs, Sunshine classics, Kahoot topic games and completed tasks on Seesaw, I found that my students need to work on their inferential skills and vocabulary. Distance learning proved that taking into account their learner identities (e.g. personal identities, cultural and social backgrounds, academic performance and learning preferences) helps improve motivation and enhance students' learning outcomes.

My next steps:
- collecting student voice: their literacy dispositions, interests and self-evaluation in reading and writing.
- finding related literacy research
- making my hypothesis