How do we design our Math Class?

I have been doing a lot of reflecting about math, in particular thinking about different types of math class situations, and considering what kinds of questions we need to ask to help students develop conceptual knowledge.

In our math classes it is important to provide students with cognitively demanding tasks. Rich tasks are great examples of this. Rich tasks provide multiple entry points AND multiple strategies that students can come to a solution.

When we are planning our math classes, we can consider the following situations that we may be providing for our students. Next, we can think about what feedback we need to make the student learning more conceptual.

Situation:

Situation #1 – Students are engaged in lessons that focus on basic knowledge, and procedures. Students need to get to a correct answer vs gaining a conceptual understanding of the strategies used. Students therefore are unable to make connections to deeper math concepts.

Key Questions:

  • What do we do to help students develop conceptual knowledge?
  • What supports need to be in place to help make this happen?

Situation #2 – students engage in more complex tasks, but then the tasks turn into procedural tasks, thus the students don’t get experience with increasingly difficult and complex tasks

Key Questions

  • How do we keep students engaged with a task, and allow them to experience increased cognitive demands and go through the ‘fits and starts’ that learners go through?

Situation #3 – Students may engage in rich tasks, with multiple entry points and multiple solution paths, however, they are unable to engage in a whole class discussion about different types of strategies.  

Key Questions

  • What steps can we take to conduct a whole class discussion?
  • How do we structure the strategies in a way that helps students to make the best connections?
  • What do we want students to get out of our whole class discussions?

Situation #4 – Students are engaged in rich tasks, with multiple entry points, multiple solution paths. Students are choosing from a variety of strategies and honing in new ones. They are able to explain why they chose a certain strategy. They are given time to explore their various strategies, and time to explain their reasoning. Whole class discussions allow for students to explore different strategies, and consider the efficiency of the strategies. Students make deeper connections, learn from peers and apply the new learning to a new task or ‘exit ticket’.

Key Questions:

  • How do we push our learning and the learning of our students in this type of a situation?

The questions can really help to guide our  thinking into how we are going to design our math class.

I would love to hear your ideas,

Deborah McCallum

Copyright, 2017

Reference

Educational Administration Quarterly

Vol 53, Issue 3, pp. 475 – 516

First Published January 31, 2017

In support of Libraries for Academic Success & Equity

Libraries are essential in building academic success and equity in our schools and learning environments. This is very easy when staff and students come from similar backgrounds and share similar languages, experiences and expectations. But what about the ‘others’? The one’s who do not share similar experiences, expectations, languages, and backgrounds?

First, what does it mean to have learners achieve academic success?

  1. Basic skills in reading, writing and math
  2. Basic knowledge of Sciences, nature, history
  3. Skills including critical thinking, analyzing, synthesizing, inferring, predicting, connecting
  4. Knowing that there are consequences for actions
  5. Flexibility
  6. Becoming a lifelong learner
  7. Participating in civic life
  8. Ability to keep up with technical changes
  9. Building confidence in a diverse and ever-changing society
  10. Adeptness at working and living with people different from ourselves
  11. Respecting cultural differences
  12. Embracing multiple perspectives.

 

Often, we as educators assume that we just need better instructional strategies to help learners achieve academic success. BUT, all of the best strategies in the world will not work if they are used in a setting where students don’t feel valued or don’t have confidence that they can succeed.

This is where Equity comes into play.

Libraries have access to resources, expertise and physical and virtual spaces to promote equity.

For instance, TL’s are skilled to organize instruction in ways that can positively build on relationships between students and classes. TL’s also provide adequate resources for students learning in first and second languages, and have the spaces to include students and value what they bring from home.

The Library also promotes citizenship, and helps students understand how we all came to belong. Library spaces have the power to address historic injustices, and connect issues of on-going colonization to the curriculum. The knowledge and resources make it more possible to engage all learners in meaningful discussions with historic specificities.

We simply cannot work with the ‘tools’ in our Libraries when we fail to understand the ‘why’ behind what we are doing.

Libraries are not about assimilation of students into dominant power structures. Rather, they are spaces with professionals who are able to analyze racial inequality, and understand that cultural differences are not temporary disadvantages that lessen over time. TL’s know that we need to go beyond ‘tokenism’ of the First Peoples in Canada. The onus is not on Aboriginal students and teachers to explain themselves.

Students who easily fit in with dominant cultural practices are fortunate to always see school reflected back to them, but TL’s know about social positioning, and work against normal power dynamics to hear all voices.

Further, new spaces, including MakerSpaces, are not used to continue to traditional narratives of education. Rather they are truly flexible and open spaces that promote other ways of expressing ideas and knowing the world around us. We don’t assume that Makerspaces are ‘what the world needs’, rather we help students make it about what they need. We help students connect them to what it means for be a respectable citizen in the world. We also allow them to be unpredictable.

Libraries provide extensive opportunities to write, talk and self-reflect.

Libraries are welcoming spaces.

Libraries encourage students to find ways of interrupting the social and ideological ramifications in which our learning is situated.

Libraries allow for discussions and assignments that trouble our already-familiar stories. And TL’s continually assess teaching and curriculum.

We know that we cannot merely congratulate white students for taking part in our national identity as being ‘helpers of the less fortunate’. Because this continues to put us in privileged positions that continue to marginalize our students.

TL’s are positioned to be aware of unconscious biases. Educators assume that we treat all students equally, but our attitudes often result in different outcomes.

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Students transfer what they know to new situations as they acquire new knowledge. This can only occur through careful planning, and active participation in school activities. TL’s are in the perfect position to help make intentional connections across settings and contexts. For instance, explicitly connecting what students learn in literacy with content areas. Ie., Connecting the reading and writing with the Science content.

Libraries are also open places for parents, and help encourage parents to safely share the language and ideas from the home. TL’s become very aware of students prior learning and literacy experiences, and work to build in opportunities for authentic communication in any language that is simply not found in any other spaces in the school.  This increases risk taking skills and develops safety and security.

We work to make challenging concepts understandable – not water down existing curriculum.

Academic Success is what we want for all of our students. However, all the best instructional strategies in the world will not help if we are not promoting equity. A signifant part of promoting equity is truly understanding the underlying philosophies of why we do what we do – and making sure that we are not doing ‘new’ things just to promote the same narratives that perpetuate privilege and oppression.

The Library is an essential space in the school that requires flexible and knowledgeable professionals who are willing and able to disrupt that which is familiar and promote equity for all.  To recognize the power dynamics that honour what is dominant, and honour other ways of knowing and being to promote true academic success.

 

 

Deborah McCallum

c2016

 

Commins, M. & Miramontes, O. (2006). Addressing Linguistic Diversity from the Outset. Journal of Teacher Education,57(3), 240 -246

Dei, G. & Simmons, M. (2010). Educating about anti-racism: The perils and desires. Our Schools, Our Selves, 19(3), 107-120.

 

 

Math: How we Teach in the Classroom Matters

Our personal schemas about math greatly impacts how we feel about math and ultimately how we will perform in math.

From the time we are born, we are impacted by the attitudes and beliefs of those around us. The effects of nurture that shape our schemas of how the world works, also shapes what we believe, how we feel, and how we perform in math.

Can you imagine the far reaching effects of math anxiety on our economy? How does society cope with copious amounts of people avoiding jobs that include math? How can we change this? First, we will look at what math is, what causes math anxiety, and where we can focus our efforts into the future.

What is math?

Math is actually a whole schema of thinking. A schema that goes much deeper than the numbers that are assigned to things in our world.

According to Geist (2011), there is a serious dichotomy between a child’s own mathematical thinking compared to that which a teacher imposes in the classroom.  How a teacher approaches mathematics instruction also impacts math anxiety in children.

What does happen in the classroom that is so different from natural mathematical thinking processes?

The following are just some of the ways that anxiety becomes built into math:

  • We associating math with boring work.
  • The work students do in class is not related to daily life.
  • We believe that if we enjoy math, then we are not learning math
  • We rely heavily on cultivating memory through rote tasks
  • Mad minute and other bell work activities reinforce the idea that math needs to be done quickly and correctly
  • We treat students as if they have the same ability in math
  • We assume that there are not preferred ways of learning math, and pace of working
  • We believe that girls achieve due to hard work and boys achieve due to talent

http://www.gettyimages.com/detail/88621772

The approaches listed above then creates an environment and a mindset that math is a high risk activity. Math therefore becomes a source of deep anxiety for many students.

The research points toward girls being particularly affected by these practices and mindsets. Further, the research also shows that environmental variables change the results of math scores of children from lower income families.

We need new strategies. We need to be sensitive to the different needs of girls and boys. The fact is that every child learns differently and responds to different types of instructional approaches.

What we can do:

  • Move away from focusing on being correct, and move toward understanding the overarching concept
  • Promote understanding of math concepts over speed
  • Foster a learning environment that allows for critical thinking processes over rote memorization
  • Implement developmentally appropriate approaches for our students vs timed bell work
  • Seek out the strategies that we know do not increase math anxiety.

 

What strategies do you use that promote critical thinking and conceptual thinking of math in developmentally appropriate ways?

References:

Geist, E. (2011). The Anti-Anxiety Curriculum: Combating Math Anxiety in the Classroom. Journal of Instructional Psychology, Vol. 37, No. 1

http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/