Thank you to Alfie Kohn, Chris Wejr and many others who have changed my thinking on awards and merit systems. They inspired change in our team.
I am a vice principal in a K-7 school with a forever tradition of Grade 7 awards night. Historically a handful of students win a few coveted awards, such as Top Male Athlete, Top Female Athlete, Top Academic, Top Fine Arts, and so on. I have never been comfortable with this tradition at our school, nor the awards nights I have attended in support of my two daughters – even if they win!
This June our grade 7 team – two amazing teachers, my principal and I, decided the time to revision, rethink and democratize awards night is NOW!
So Why Rethink Awards?
- We are comparing apples and oranges. Students do not start at the same place, with similar opportunities and levels of support. If they did, then there might actually be something to compare – if that mattered here….For our high achieving students who anticipated winning an award, this idea helped them recognize that awards aren’t really “fair.”
- Student success is more than a letter grade. We are involved in a Communicating Student Learning Pilot in British Columbia and do not currently give letter grades in Grade 7 at our school – but the vast majority do. Justifying grades or percentages – sometimes to the second decimal place – for awards is a practice fraught with problems. (Think quality assessment, formative / summative, grades that are meaningful, accurate and consistent across the school, the District, the Province, etc.)
- Every student deserves acknowledgment that is not ranked. Our grade 7 teachers worked with their students to create categories of recognition and criterion for each category. They used a Google doc to gather students’ responses. They asked students to identify where they and a randomly drawn peer would fit best, and why, and what category they would be most proud to receive. Teachers read these and discussed them with the students. All but a few students expressed that this was fair, and felt like it honoured and respected all students.
- Alignment with your core philosophy matters all year. Our teachers worked all year to intentionally create a community of learners based on trust, respect and care. The idea of honouring a handful at the end of the year felt antithetical to our core work and beliefs.
- Competition can be exclusionary and harmful. Of course competition exists in the world and students will need to learn to maneuver that. Teachers can help! But school is not a training ground for students to get used to exclusion and defeat. Rather, it is a tremendous opportunity for students to experience being part of a community who cares, and to learn the life skills to get there.
A Happy Ending…
We replaced the old plaques and cups that brandished one name per year with a single wooden plaque that read Class of 2015. Each category had its own metal plate and the names of students who earned that recognition. Every students’ name was on the plaque. At the end of the night, many parents took a photo of the plaque and posted it online. Some told us that they never thought their son/daughter would ever win an award at school.
To our courageous and trusting grade 7 teachers for pioneering, and traveling together on this journey. It was a tremendous amount of work for them, and we are very proud and appreciative!
A Word of Advice
Give parents and students ample notice that you are going to change the practice and invite feedback. We did this via a letter to parents (see below) and ongoing conversations with students. However, we did this very late in the year and discovered while we had been thinking about this change for years, the students and parents had not!
This post has been swirling around in my head since May. A nod to @wcarozza for gently prodding me to blog already! Please check out his fantastic blog, Principal Reflections.
Grade 7 recognition letter_June 2015
Enjoyment appears at the boundary between boredom and anxiety, when the challenges are just balanced with the person’s capacity to act. ―Mihaly Csikszentmihaly
This week in music class my students and I experienced our first state of flow. It was enthralling! I had not expected this at all, but simply wanted to reintroduce the xylophones to the students in a way that would capture their interest and engage their sense of play and curiosity. I asked the students to work in pairs to create a pattern (or two interlocking patterns) on the xylophones that was inspired by a drawing of a rainbow or waves. They were simple line drawings, and after modeling this with students and talking about the pattern coming from our imagination (There is no right or wrong way to sound like a rainbow….), we talked about how we could remember our pattern for next class. “We could write it down!” someone said. Exactly. But how? Well they had many ideas. And their investment in creating the patterns, notating them in their invented notation, revising and adding descriptive detail to their very first musical scores was fascinating to observe. They were completely absorbed and focused. This was not something I see every day in music class!
Csikszentmihalyi, the architect of the notion of “flow” says creativity is a significant source of meaning in our lives. “When we are involved in creativity, we feel that we are living more fully than during the rest of life.”
You can listen to Csikszentmihaly’s TED talk: Flow, the Secret to Happiness here.
Our classes are 30 minutes long and usually involve a variety of activities for the young students, including transitions in and out of the room. This process took numerous lessons and they just entered the room and got straight to work. The students were so eager for me and for their teachers to hear their compositions and see their scores that we ran overtime with every class. The students played with obvious pride. And they watched and listened to each other with interest. I was so engrossed in listening to students as they made numerous musical decisions about what to play, how to play, and how to remember their patterns for next class that I would glance at the clock, surprised to see that our time was up.
Why Flow? Why Now?
As I reflected on our classes and thought about why these lessons were so engaging for the students, several things were clear.
The students had agency and voice. They created their own patterns (within some boundaries), and they had to create a system to write these down. Perhaps it was partly the act of writing their patterns down that gave the notes permanence, a special significance, or perhaps it was simply the creative endeavour of inventing a system to write music that they found interesting.
The students collaborated. Most students chose to work alongside another student to bounce ideas back and forth, to play in the spaces the other left behind and to feel the common pulse of the music. There is joy in this process of discovery when we improvise and the rhythms connect, the patterns fit together, we share something special and unique.
Every student had the opportunity to struggle. At a recent Gifted Education conference I attended, the speaker reminded us that every child deserves to struggle. It is our responsibility to ensure that the tasks we offer are flexible enough for children to work at their own level of challenge, whether they are at an emergent stage of development or a proficient stage. This fosters engagement.
Students were motivated. The tasks were improvisatory and creative. Students could express themselves with their compositions, share them and since there was no right answer, it presented a low risk way to enter into improvisation. And it was FUN!
The students were at the centre. After initially explaining and modeling the tasks, the students were focused on listening, composing and notating. I was there to listen, to offer suggestions and ask questions.
I was surprised at how quickly and easily the students slipped into what looked and sounded like a flow state. The tasks were not particularly special or unique, yet they captured the students’ imaginations and their sense of play and wonder. Now I find myself wondering, how can I keep this state of flow alive while preparing for a winter concert and beyond? A question worthy of some thought and conversation!
Here are more pictures of the students at work. Also, take a look at the variety of scores from students in grades 1-4. It is a fascinating glimpse into their thinking.
You know that what you need to do is possible to do, even though difficult, and sense of time disappears. You forget yourself. You feel part of something larger. —Csikszentmihalyi on experiencing ‘flow’
If you would like to see my Music Teacher’s Blog please click here.
If you are like me and you believe in active music making in your music classes, you might wonder how technology can benefit your program. Here are some ways that technology has deepened musical learning in my classroom:
1. Practice Ongoing Assessment and Feedback for Learning
We can use an iPad or iPhone to take snapshots or video of students as they are engaged in the music class. At first, I thought it would be impossible to free myself to do this, but I found that with guidance and a specific focus, even our youngest students can sing an action song, practice a pattern, work with a partner or practice using an instrument while I record their work. We can hook up to an LCD projector, or gather around the iPad to watch and listen immediately. This is a great opportunity to discuss what is working, what needs improvement and ways to improve. Talk about timely and useful feedback! Students really enjoy seeing and hearing themselves; as we all know, it is a different experience to be INSIDE the music, then to be outside of it. Older students can use these opportunities for written or verbal self and peer evaluation.
2. Share our Learning Beyond the Classroom Walls
Post pictures and videos, discoveries and questions from music class on your class blog or your school’s website. Parents will have a greater understanding and interest in your music program when they can see inside the “black box.” Students can share their learning with the school, their family and other students anywhere in the world. Post excerpts from your performances for all to see. It is highly motivating for students when they have an audience beyond the classroom walls.
3. Connect and Communicate
After launching my music class blog, musicisawesome.ca, my students started to comment on the posts, ask questions and share ideas. So did their parents, and siblings!
The teacher can moderate all comments before they are posted and respond to student comments or questions, providing another way to connect with students. This is especially meaningful when we teach 30-minute classes twice a week and don’t always get a chance to connect with individual students. Online sharing also allows students who may not always feel comfortable speaking out in class, or need more time to respond, to post their thoughts.
4. Access a World of Musical Resources
Technology in the music classroom affords us access to endless resources, from authentic music performances and demonstrations from all over the world, to symphony performances and rehearsals, interviews with conductors, and the opportunity to hear sounds of individual instruments or instrument families. Share variations of classroom repertoire for students to see, discuss, compare and critique.
5. Engage and Invite
Introduce a unit or lesson with a brief video clip to increase student engagement and anticipation of the learning ahead. For example, introduce a unit on found sound with a few excerpts from STOMP or launch your marimba piece (played on ORFF barred instruments) by sharing and comparing traditional marimba groups and other school groups performing the piece.
6. Empower Students to Be Musical Curators
Students can search for interesting musical sites, ideas, cool songs, bands or performances, such as creating a music wall or watching a performance of ice rhythms played on a frozen lake! Students will search their favourite sites to discover new and interesting things to share with their peers. After we learned the Cup Song, a number of students searched YouTube and found instructional videos and many variations of the song. Many students used the videos to help them teach the pattern to their families.
7. Honour the Principles of Learning
People learn at different rates and in different ways. This we know! When I post instructions to a game, words to a song, pictures of our music charts or song maps, students can use these to practice, to review, to think about, or to discuss with others. Students can watch videos and practice at home, or teach their siblings or parents. For some students, the benefit of accessing the classroom materials at home allows them to learn through repetition, at their own pace. Highly visual learners also benefit from using technology in class, where we can see animated charts or stories and songs.
8. Use Skype to Connect and Share
With Skype, we can take a field trip anywhere – for free! We can bring a composer or musician into the room when funds do not allow us to bring them in person. We can also Skype other music classes, share songs and games, homemade instruments or special activities. I started this venture with my extraordinary music teacher colleague who teaches music at Mamquam Elementary in Squamish BC. We planned some of the same activities together and will be using Skype to visit each others rooms and invite the children to watch and discuss the variations in our activities. Stay tuned for our versions of Stone Soup!
9. Take a Soundwalk or Compose a Soundscape
If your school has iPads, even a few, students can take a soundwalk in the school, or outside the school in pairs or small groups. Using the record function on the iPad, students can capture sounds they find interesting. Students can share their sounds and use them in a composition, either through Garageband or for a class composition. The sounds can be organized, arranged and used with instruments to create sound carpets or accompaniments to stories or poems.
How do you use technology in the music classroom?
Creative Commons photo by Wha'ppen
How can we give ALL students access to rich materials and curriculum? We can Teach Up!
Since my daughters entered public school many years ago, I have been thinking about the provision of high challenge, high interest curriculum. (It seemed scarce some years…) So where are kids most likely to encounter rich and engaging materials and tasks? No surprise – research tells us it is typically in high socioeconomic schools where there are not significant barriers to learning such as poverty and homelessness. In these schools, teachers are often experienced and well resourced. In these schools, it is least urgent.
Teach Up for Excellence by Carol Ann Tomlinson and Edwin Lou Javius (2102) brings our attention to the dire need to provide ALL students with “equitable access to an engaging and rigourous curriculum.” (note: you must be an ASCD member to access full article. It’s worth a subscription!)
What is Teaching Up?
The Seven Principles of Teaching Up, based on Tomlinson & Javius, are listed below. To what extent do you believe in and enact these principles in your teaching?
1. I accept that human differences are not only normal but also desirable.
I work to intentionally create a community of learners in my classroom.
2. I believe in the capacity of each child to succeed.
This reflects a growth mindset: the understanding that effort, rather than any other qualifiers matter most for student success. For more on this, read Dweck’s Mindset (2007).
3. I work to understand my students’ cultures, interests, needs and perspectives.
Tomlinson notes, “understanding students’ learning profiles is the driving force behind instructional planning and delivery.
4. I create a base of rigorous learning opportunities.
I find ways to connect kids to content in meaningful ways. Our tasks are authentic and challenging yet do-able.
5. I understand that students come to the classroom with varied points of entry into the curriculum and move through it at different rates.
6. I create flexible class routines and procedures that attend to learner needs.
7. I am an analytical practitioner.
I am always reflecting on the successes and challenges of my students and modifying to better meet their needs.
Hope and Love is Not Enough!
While we care deeply for our students and hope each and every one succeeds, Teaching Up requires that we are strategic, explicit and purposeful in our practices. While it may be tempting to “hold back” exciting work or projects until a student finishes the teacher tasks (some never do!), or give lots of extra worksheets to practice “the basics” for struggling students, we risk further jeopardizing our most vulnerable learners. Tomlinson & Javius note, “When lower-performing students experience curriculum and instruction focused on meaning and understanding, they increase their skills as much as their higher achieving peers do” (Educational Research Service, 1992). Every child deserves access to interesting, meaningful activities, varied resources and real-world problems to solve.
The article concludes, “Teaching up is not about hope. It is about purposeful instructional planning that aims at ensuring high-level success for each student.” Every child at every school deserves the best chance for success.
Matsuri by Kaya Newman
It is late summer. I can feel the rhythm of many summers past – insistent, humming – yet now it is time to begin. My new position is vice-principal at a K-7 school with a district Fine Arts Intensive program.
I will also be teaching music 3 days/week as well as other teaching duties on a fourth day.
I have had the great privilege of working as a district-based helping teacher and have worked with many teachers and staffs supporting quality assessment, engaging instructional practice and helping to connect kids meaningfully with big ideas in the curriculum. The moment of change, I remind myself, is the only poem.
I stand now at this crossroad and contemplate the complexities of the work before me. Peeling back a layer, I wonder how I will realize the big educational goals that I value in my music class. Our district structure delineates 30-minute music classes (up to 9 classes per day). Music educators facing a new school year may be thinking about similar questions, such as:
- How can we build lessons that are authentic, personal, and important?
- How can we ensure students have ownership of their learning?
- How can we connect to the passions, interests and experiences of nearly 300 students?
- How can we embed 21st century tools, skills and opportunities to share and connect with the global community?
- How can we ensure our public performances are authentic, reflecting the children’s thoughts and ideas, rather than the teacher’s vision?
As the year unfolds, I will grapple with these questions as many of you will. I hope to encourage, guide and allow space for the children to create and imagine. I hope to…
- focus on what the students are learning, rather than what the teacher is doing
- blog and share our work with parents, families and the greater community
- use social media to connect with musicians, music teachers and students
- explore digital technology where it makes sense to compose, create, critique, listen and share beyond the classroom
Please share your ideas on how you accomplish authentic and engaging learning in the music classroom…..we have so much to learn from one another!
Dr. Charles Leadbeater has some very interesting insights into education and innovation. He spoke to a large group of CoastMetro educators at the Italian Cultural Centre on February 17, 2012. The event, “Redesigning Our System to Personalize Learning: lessons learned and disruptive innovation in education” highlighted innovation from some unusual vantage points.
As an advisor to the UK Innovation Unit, visiting senior fellow with the British National Endowment for Science Technology and the Arts, among many other groups and organizations, Leadbeater’s work centres on culture, innovation, creativity and change.
Are YOU an Innovator?
Leadbeater shared a simple graphic to illustrate his thinking about what it takes to be an innovator:
- A person who BELIEVES and BEHAVES is a FOLLOWER
- A person who DOESN’T BELIEVE and DOES BEHAVE is a COMPLIER
- A person who DOESN’T BELIEVE and DOESN’T BEHAVE is a REBEL
- A person who DOES BELIEVE and DOESN’T BEHAVE is an INNOVATOR
Leadbeater described an INNOVATOR as someone who is committed to a deep vocational purpose, such as an approach to teaching and learning, who does not behave, that is, they are “brave enough and odd enough to challenge deeply held conventions.”
If you embody the beliefs and behaviours of an Innovator, Leadbeater noted that people will likely think you are “quite mad half the time.” And of course the possibility exists that you might be quite mad all the time. However, he described the future of our education system as being “in the hands of those who will disrupt it in important ways.” A fine line here, but one worth ducking under, stepping over or going purposefully around.
The Eureka Myth
According to Leadbeater, innovation is highly derivative, cumulative over a long period of time – a mixture of inventing and borrowing. It is highly collaborative, involving old and new ways of thinking. The Eureka Myth is simply that – a myth. As educators strive for highly collaborative, purposeful teaching and learning environments, embrace the use of “both, and” (for example, think analog, digital and whatever we create), we are well on our way.
Innovating through Technology
Leadbeater described children as just soaring with technology; they think of it like they do water. Whereas we want to don a wetsuit, flippers, mask and fins, the children just jump in. I am keen to dive in, splash alongside, and explore the rich environment. I know someone will throw me a rope when I need it. How about you?
87 as the synapses fire you see by Richard Lazzara
Getting up at 6am on a Saturday is not part of my usual weekend routine. But I did just that on January 14, full of anticipation for the day ahead.
I was off to edcamp43, an “unconference” hosted by Coquitlam educators, where those passionate about education gather, set an agenda in real time, choose topics of interest and dig into small group conversation.
There are no facilitators, presenters, speakers; no pre-set agenda. The format is highly personalized; participants have choice, voice and agency. The democratic structure and the presence of many committed, passionate and interesting educators, parents and students made the day a remarkable one.
Why go to edcamp?
1. Possibilities Abound
I was excited by the endless possibilities of how the day might unfold, similar to the feeling I get before a jam session with musicians I have not yet played with.
- would the topics we select be relevant and deeply interesting?
- how would I meaningfully participate?
- would the connections with others be sustaining and important?
2. Relevant, Engaged Learning
Have you ever gone to a pro-d session and scanned the workshops thinking hmmmm…..is there anything here I am really excited about? This was not a problem at edcamp. Everyone had a voice in generating topics and selecting their sessions of interest. I was keenly interested in all of the topics and ultimately chose Inquiry, The Transformative use of Technology (along with many others, see sticky note below) and Are Report Cards Necessary? (I did worry briefly that the latter session would last about 23 seconds – but the conversation was terrific….)
3. Democracy at Work
With no table facilitators or session leaders, we were on our own for rich, small group discussion–emergent content at its best! Teachers, parents, students and administrators came together to discuss what matters most in education.
4. Build and Strengthen your PLN
I connected with colleagues from across the lower mainland and beyond, as well as a number of folks I had only met through twitter. Social media definitely has an important place in building and sustaining our professional learning networks. Edcamp provided a great opportunity to meet f2f with educators I connect with in virtual spaces.
Also, as Darcy Mullin noted in his post edcamp post, it is a highly worthwhile event and it is virtually free.
Yeah, but doesn’t it all boil down to the conversations?
Yes and they were extraordinary! The conversations were so rich and interesting– one participant, Brian Kuhn tweeted that edcamp is “the hallway conversation on steroids.” Here are a few highlights:
INQUIRY – Loved that we did not feel a need to define inquiry but spent time talking about how it can be a powerful mode of learning – for adults and children. We wondered:
- How will children involved in inquiry change their orientation to learning?
- Will children ultimately demand more relevant, robust learning from their teachers?
- Who does the work in an inquiry classroom? What might this look like?
- How can we manage the persistent need for change?
Surrey’s Jonathan Vervaet brought two of his grade 11 students to camp. One student described how he did not really like Mr. V at first; he was used to doing worksheets and this inquiry stuff was different and hard. But that all changed. His next comment caused the room to fall silent: “We had to actually think when doing inquiry in Mr. V’s class.”
THE TRANSFORMATIVE USE OF TECHNOLOGY – Themes were leveraging change, promoting growth, shifting power, explicit teaching (for both adults and students), the importance of using both digital and analog tools for learning (whatever best fits the purpose and the student’s needs and interests). Peppering the conversation was the enthusiastic sharing of blogs, twitter groups, websites and individuals leading change in this area.
ARE REPORT CARDS REALLY NECESSARY? This was a great conversation on formative and summative assessment–what do these mean and why do they matter–for all stakeholders. We discussed the positive outcomes as teachers have found creative alternative ways to share student achievement with parents and students. It is the “and students” part that I find particularly exciting!
Aaron Mueller shared some of his thinking from a Distance Learning perspective:
- introducing himself to students through video blogging (what a great idea for any teacher!)
- learning that allows unlimited submissions as students work toward mastery (this practically led to a standing ovation for Aaron in our small group!)
- the establishment of a private YouTube channel for ongoing feedback and connections with students and families
Thanks to the terrific organizational team from Coquitlam for hosting edcamp43!
by Alicia Logie
As I have developed as a teacher-learner, particularly as assessment and evaluation began to occupy more and more of my thinking, I began asking myself the question: What do I learn from the assessment/evaluation I do with my students?
And also, what do THEY learn from the assessment we do in class?
So recently, with the group of adult students taking a course (in French) on Evaluation and Assessment in the Classroom, I asked them to tell me what they had learned. Half of the students were practicing teachers and half were teacher-candidates in their first semester of studies. What they related spoke of the powerful changes that had happened over the course of our time together. I had decided to model one of the effective strategies for assessment and grading that we had discussed, so for their last class I conducted evaluation conferences where each student had 10-15 minutes to summarize their learning, speak of future goals and negotiate a mark with me.
My Students’ Learning Goals:
I am going to focus more on the learning and less on the marks.
I am going to do more formative assessment and less summative.
I am going to remember that the marks do not motivate the learning, the descriptive feedback does.
I am going to give students more practice time, include them in their assessment and collaborate on criteria for assignments.
I went into a conference with parents who are quite difficult and I felt calm and confident. I tried to figure out why- in the past I would have been nervous and anxious. I realized I now had confidence; confidence that I had all the information I needed to accurately and meaningfully discuss the progress of their child, that there was research that backed me up, that I am not the only teacher who assesses this way- there are many of us! And we are doing the right things!
I am going to remember that it is about the learning!
My Learning Goals:
I learned that looking at real examples of good assessment practice in action – TOGETHER – is what gives us the courage to assess in ways that support student learning. My goal is to continue to create opportunities for dialogue that expand our thinking, and give us courage to change.
Alicia Logie is the French Immersion Helping Teacher (conseillere pedagogique) for the Surrey School District. She also teaches university level teacher-training courses.
Working and learning with education students as they grapple with what it means to be a teacher is tremendously rewarding. My experience as a Faculty Associate was just over two years ago and I now have opportunities to work alongside former students – colleague to colleague.
I recently visited a former student’s classroom and was in awe of her skill, instructional practice, and rapport with her students. We no longer spoke about the basics of managing the class, setting a purpose for a lesson or building trust and relationships with students, staff and parents. Instead, Ms. S and I tackled deep issues about teaching and learning in the year 2011:
Scaffolding vs. Teacher Control
Ms. S is working intentionally and thoughtfully towards increasing student ownership of learning. She has many structures in place to do so, such as providing students with choice in how they demonstrate understanding, setting their own timelines, and gauging their own readiness to move on. Yet, like so many teachers, Ms. S wonders whether she is over-managing the learning environment or simply scaffolding for success.
In our teacher education module, we explored the notion of “enabling constraints.” I discovered the term in the book, Engaging Minds. Enabling constraints are about opening possibilities by limiting choices.Very simply put, too much choice is overwhelming. Too little choice is restrictive, squelching learning and creativity. By giving choices in lesson activities and projects within a given structure we are providing enabling constraints.
Enabling constraints are not prescriptive; they don’t dictate what MUST be done, rather they are expansive, indicating what MIGHT be done… from Engaging Minds (2000), Davis, Sumara, Luce-Kapler, p. 193
At the university, we investigated this idea by giving groups of student teachers a bag of Lego and instructions. The instructions ranged from one word: Build to more detailed instructions such as Build, but a red piece must touch a yellow piece, a green must touch a blue and your structure cannot be more than 5 cm tall. In our debrief, students noted that too little information was discomforting, they were not sure of the purpose or success criteria. Too much information, on the other hand, limited creativity and imagination. When teachers frame a question or task using enabling constraints, we allow for flexible, responsive teaching and learning.
Continue reading Things I Learned From My Student Teachers [part 112.63]
Last week we had over 80 parents, along with administrators, thinking, doing and talking about math. The event was a School Planning Council meeting sponsored by our district, facilitated by Richmond educator and consultant Carole Fullerton. She has developed an excellent blog, Mathematical Thinking.
She began by asking parents what they wanted for their children. They responded with similar ideas across the room:
• to enjoy and be engaged by math (not to fear math)
• to connect with their learning
• to understand math (not just memorize procedures)
• to be able to use what they know about math to solve real problems
A couple of big ideas that stuck with me:
1. Teach Math from Left to Right
When we do mental math (add, multiply, divide, or estimate in our heads) we tend to perform the calculations using the largest numbers first. For example, if I needed to add 86 books to 73 books, I might think 80+70 = 150 and 6+3 =9, therefore my answer is 159. There are of course, other ways to think of this, but that is one way.
Why then, when we add or subtract numbers on paper do we begin with the ones column and move from right to left? When parents posed this question to Carole, she cited convention. It is simply the way we’ve always done it, but it is not the best way according to Carole. She added it is the only thing we do in this order in English . . . Carole modeled how teachers and students can add, subtract and solve various problems by thinking and working from left to right – just as if we were solving the problem in our heads. The beauty of thinking and teaching in this way is that the mental process mirrors the written process, and facilitates a much stronger number sense.
Continue reading Doing Math: from Left to Right