Surface learning – setting the foundation

The instructional goals of any lesson need to be a combination or balance of the three phases of learning – surface, deep and transfer. An expert teacher knows when and how to help students move from surface to deep and transfer learning. Despite whatever phase of learning the two key reminders are:

  • Learning intentions and success criteria need to be clearly signalled.
  • The instructional strategy with the highest importance is student learning.

Surface learning is the focus of Chapter 4 of Hattie, Fisher and Frey’s text Visible learning for mathematics. When students are at the the surface phase of learning, high-impact approaches that foster initial conceptual understanding are followed by linked procedural skills. The tasks are efficient, often more engaging and designed to raise student motivation. When considering the fluency quadrant, many tasks will be of low difficulty and low to moderate complexity. There should be discussion and opportunities to connect the tasks to students’ learning and understanding.

…observing someone doing something uses many of the same neural pathways as when you perform the action yourself.  (Hattie, Fisher and Frey, 2017, p107).

One of my favourite references. Number talks helping children build mental math and computation strategies by Sherry Parrish

Making number talks matter by Cathy Humphreys and Ruth Parker

This is why number talks, guiding questions, worked examples and direct instruction are so powerful. I am not going to go in-depth into these as the text does it beautifully. What I will say it that I was first introduced to number talks a couple of years ago when I was doing some work around the development of mental calculation. I became an immediate advocate and have bought a number of texts that illustrate how number talks are conducted.

I will also mention that direct instruction is especially useful in developing students’ surface-level learning but it has the following caveats. It should not:

  • be used as the sole means of teaching mathematics.
  • consume a significant part of the instructional time available for learning.
  • always have to be used at the beginning of a lesson.

All four activities enable teachers to demonstrate the kinds of questioning and listening strategies that exemplify excellent mathematical practice as well as give their students opportunities to begin building these habits of mind (Hattie, Fisher and Frey, 2017, p119). Self-verbalisation and self-questioning, skills that help students think critically, have an effect size of 0.64. The text also provides some simple sentence frames that can be used to facilitate student metacognitive thinking (which has an effect size of 0.69).

In the last part of the chapter, the authors consider how to use vocabulary, manipulatives, spaced practice with feedback, and mnemonics strategically.

Vocabulary instruction is important in all the phases of learning but it is often in the surface phase that students begin to build academic language. Researchers such as Beck that as teachers, we need to support students in the appropriate terminology but not give away the mathematical challenge. A focus on vocabulary has always been a focus in the work my colleagues and I have done in mathematics and numeracy. There are many vocabulary games that can be used in warm-up or transition times and we have always promoted the use of word walls and graphic organisers, the latter two being addressed in this chapter.

The CSA model used for problem solving strategies

Using manipulatives in all the learning phases helps build the links between the object, the symbol and the mathematical idea. It has an effect size of 0.5. Once again, my colleagues and I have promoted the use of manipulates and have commonly referred to the Concrete Semi-abstract Abstract (CSA) model.

Using the dual approach of spaced practice and feedback teaches students about the task and about their thinking. Spaced practice, giving multiple exposures to an idea over several days to attain learning and then spacing the practice of skills over a long period of time, has an effect size of 0.71. Feedback about the process (and not just the task) moves students into deeper learning and has the added advantage of giving a student agency so that they rely lesson on outside judgments and have a more positive mindset.

The use of mnemonics has an effect size of 0.45 and assist students to recall a substantial amount of information.

The authors give readers an insight into research based tasks that have a high effect size in the surface phase of learning. This strong start sets the stage for meaningful learning. Too often, however, the learning ends at the surface level. Teaching for deep and transfer learning must occur. My next blog will look at making learning visible in the deep learning phase.

Hattie, J., Fisher, D., & Frey, N. (2017). Visible learning for mathematics What works best to optimize student learning Grades K-12. Thousand Oaks, CA: Corwin.

 

 

Making learning visible in mathematics

Graduation – Masters of Education 2005

 

How does one become a lifelong learner? How do we develop a love of learning? Hattie, Fisher and Frey (2017) argue that making learning visible assists teachers and students to become lifelong learners with a love of learning. I am proud to say that I am a lifelong learner (as signified in the name of my blog).

After reading the first chapter of  Visible Learning for Mathematics, I spent some time considering how my passion for learning came about. I came to the conclusion that I was lucky enough to enter a profession that I love: one that involves constant re-invigoration and one with which I have a natural affinity. I was also lucky to have two brilliant mentors in my education: my English teacher in year 11 and 12 (Mrs Kay Gardiner) and my Children’s Literature lecturer when I completed my Bachelor of Education (Professor Kerry Mallan).

The above-mentioned ladies were instrumental in my love for English and literature and yet I ended up spending four years of my career specialising in numeracy and mathematics.  As mentioned in my previous blog, I have always loved the challenge of mathematics but was never very successful in my P-12 grades. My experiences were very much ‘chalk and talk’ and the learning of procedures and formulas. I then struggled when it came to applying those procedures and formulas in a test.

Hattie, Fisher and Frey stress the importance of teachers erasing many of the ways they were taught mathematics and replacing this with intentional instruction, collaborative learning opportunities, rich discussions about mathematical concepts, excitement and persistence when solving complex problems, and applying ideas to situations and problems that matter. I can certainly concur with that – my understandings, application (and marks) would have improved considerably in a classroom such as this.

The first chapter of  Hattie, Fisher and Frey’s book looks at making learning visible for both students and teachers; the debate between direct instruction and dialogic approaches; and the balance of surface, deep and transfer learning.

Hattie, Fisher and Frey write that visible learning:

  • helps teachers identify the attributes and influences that work.
  • helps teachers better understand their impact on the learning of their students.
  • helps students become their own teachers.

    http://www.jjfbbennett.com/2016/04/visible-learning-quotes.html

When it comes to the two approaches of direct instruction and dialogic, both focus on students’ conceptual understanding and procedural fluency and neither advocates memorising formulas and procedures. Both models suggest:

  • designing mathematical instruction around rigorous mathematical tasks.
  • monitoring student reasoning.
  • providing many opportunities for skill- and application-based experiences.

Differences include types of tasks, role of classroom discussion, collaborative learning and role of feedback. Hattie, Fisher and Frey (2017) have put together an explicit table that explores the similarities and differences of both approaches and how ‘knowing what strategies to implement when for maximum impact‘ is precision teaching (p26).The authors state that it is not a choice of one approach over the other. Both have a role to play throughout the learning process but in different ways.

Finally, Hattie, Fisher and Frey address the balance of surface, deep and transfer learning. Surface learning provides the toolbox of conceptual understandings, procedural skills and vocabulary and labels of a new topic. It helps students develop metacognitive skills and can be used to address student misconceptions and errors.  Students need this toolbox but there is often an over reliance on surface learning and the goal is much more.

Deep learning is where students begin to consolidate understanding of mathematical concepts and procedures and begin to make connections among ideas. This is often accomplished when students work collaboratively, use academic language and interact in deeper ways with ideas and information.

Transfer learning is the ultimate goal. Students have the ability to take the lead in their own learning and apply thinking to new contexts and situations. They are self-directed with the disposition to formulate their own questions and the tools to pursue the answers.

As a classroom teacher, I was eclectic. I believe I used different pedagogical practices and had a balance of direct and dialogic approaches but it was more instinctive rather than intentional and precise. I believe I spent too long in the surface learning. Deep and transfer learning would have happened to some degree but I don’t believe it was always intentional.

As teachers, we have choices. Understanding these phases of learning assists us to make instructional choices that will impact student learning in a positive way.  Hattie, Fisher and Frey’s text helps with precision teaching and my next blog will look at the second chapter that focuses on teacher clarity. Until then…

Hattie, J., Fisher, D., & Frey, N. (2017). Visible learning for mathematics What works best to optimize student learning Grades K-12. Thousand Oaks, CA: Corwin.

Vocabulary

Understanding the Reading Process – The Big Six

my powerful words

My powerful words poster for a week

In my role, I deliver a lot of professional development and I love presenting a session on vocabulary. I was lucky enough to ‘inherit’ an original professional development session on vocabulary from my mentor and friend, Kay and her colleague, Chris. Over the years, I have delivered several vocabulary sessions and I don’t think any one session has been the same.

I am always reading new research and incorporating new ideas and strategies and there are a couple of ideas in Konza’s papers that I will use in a session I am running in a few weeks.  In today’s blog, I will be summarising Konza’s synthesis of research on vocabulary, both from her original paper and the supporting vocabulary paper.

Vocabulary

Bromley (2007, p 528) wrote vocabulary is a principal contributor to comprehension, fluency and achievement. Vocabulary development is both an outcome of comprehension and a precursor to it, with word meanings making up as much s 70-80% of comprehension.

Vocabulary is a key component of reading and if students know the meaning of a word, there is far more chance that they will be able to read the word and make meaning of the sentence. Vocabulary is generally learnt indirectly through repeated exposure – conversations, listening to stories, reading and through the media.

Some children will arrive at school as highly competent vocabulary users and will absorb words easily. They will be more likely to acquire the skills of reading easily and thereby continue to build their vocabulary knowledge. Other children come to school with small vocabularies and are often not skilled in learning new words, have a more restricted range of words and less access to the vocabulary of books. Consequently, they are more likely to have difficulty acquiring the skills of reading and will be unable to use the skills of reading to develop vocabulary further.

A number of researchers have found that direct instruction is effective for vocabulary growth in all students. In primary school, a rich bank of words that permeate across many contexts needs to be developed. ‘Rich and robust’ (Beck & McKeown, 2002) vocabulary development entails careful choice of words for instruction, strategies that develop deep understanding, regular use and an increasing ‘word consciousness’ in all students. Biemiller (2010) recommends teaching as many new words as possible and Pressley et al (2007) advocates ‘flooding’ classrooms with a range of long-term vocabulary interventions. Konza’s paper on vocabulary includes guidelines and strategies from all three ‘schools of thought’.

Guidelines and Strategies for Vocabulary Development

1. Build vocabulary instruction into everyday routine

  • model high quality language.
  • incorporate vocabulary building into directions and teaching.
  • organise frequent small group interactions to build oral language.
  • preteach critical vocabulary.

2. Select the best words to teach

  • Konza lists 5 questions that will help with word selection (see her paper).

    vocabulary in maths

    Some tier 2 and tier 3 words for a year 2 maths unit

  • There are three tiers of words: Tier 1 – basic and high frequency words; Tier 2 – words that appear more frequently in text than in oral language and   are less likely to be learnt without assistance; and Tier 3 – subject specific words.
  • Tier 2 words should be the focus of direct vocabulary instruction – maximum of 7-10 Tier 2 words from any one book or piece of text.

3. Explicitly teach word meanings

  • Read aloud the sentence and show the word.
  • Have students repeat it several times – brainstorm meanings – look for helpful parts – reread the sentence.
  • Explain the meaning with a student-friendly definition and synonyms.
  • Provide examples.
  • Ask questions to determine understanding.
  • Provide sentences that students can judge as being true or false.
  • Students write own sentences to be judged true or false.
  • Consciously use the word throughout the following days.

4. Teach students to use contextual strategies

  • An example are words that may be in bold or italics – indicates important or new terms and are often explained in a glossary.

5. Teach students to use graphic organisers to explain word meanings

  • using concept maps, word trees, word maps and Y charts are different ways of explaining word meanings in detail.
  • help students develop a clear and accurate concept of a word.

    instagrok

    Using the online instagrok to form a word map

 

Goal

The goal is to develop ‘word consciousness’ – enjoying learning new words and using them in different ways. Teachers who appreciate and enjoy words and understand the power and value of a rich vocabulary pass that enthusiasm and knowledge on to their students.

The word snoop

Enjoying the English language