Lesson Planning For Algebra

When lesson planning it is of the utmost importance to take as many things into account as possible in order to avoid a lesson going awry and becoming uncontrollable and resulting in misunderstandings or no absorption. There are many factors to account for such as, possible misconceptions& lack of prior knowledge& behavioural issues& and the level of accessibility to students, just to name a few. Whilst thinking about what could go wrong, it is very common for teachers to get bogged down in the negatives rather than the positives that happened in the last lessons& something I learned against in a recent CPD session: in order to make improvements and learn from mistakes, teachers must consider the methods of improvement and not dwell on the problems& using the same question If I could teach that lesson again, what would I do differently? In a way, this constructive self-evaluation is similar to the assessment for learning that we use to monitor progress and understanding of students within lessons.

Misconceptions are a very common problem that teachers have to consider and overcome when it comes to teaching, especially when it is a topic that is a deeper study of something learned before. I read before that the typical chain of poor maths knowledge that students experience starts with an error& soon followed by misunderstanding, which, in turn, leads to misconception. In a perfect world, there would be no misconceptions as any errors that a student (or easily a teacher too) makes would be addressed and solved as and when they become apparent. In the real world however, all too frequently are incorrect answers misheard as correct, or different methods mixed up and used in the wrong ways& as a result, it is pertinent for teachers to be able to plan ahead for any possible misconceptions (pre-existing problems) and errors (potential problems). Within the topic of algebra there are a great many possible misconceptions due to the simple fact that algebraic manipulation calls upon a plethora of knowledge and skills from a range of other maths topics.

More often than not, errors with brackets are exhibited by students that have not fully grasped the concept, or have struggled to finalise an algebraic statement in their mind. Typically the main error is missed/assumed parenthesis, especially when powers are included in the problem. There are 4 main examples I am aware of: the case of raising a term with a coefficient to a positive power (integer and fractional)& raising a negative number to a positive integer power& and subtracting a whole polynomial from another, as detailed below.

Case 1: Cube 3x

Whilst the correct answer is 27x^3, the common mistake made is not apply the power to both the coefficient [3] and the term [x] resulting in the answers 3x^3 or 27x.

Case 2: Fourth root of 16x

2x^(1/4) is correct as the fourth root applies to both the coefficient 16 and the x term, many students still apply the power to only one of either the coefficient or term: resulting in one of the following two answers& 4x or 16x^(1/4).

Question 3: Square -4

-4 squared is obviously 16, however several children have the misunderstanding that the 4 is squared and the negative sign is given afterwards& not associating that minus to the 4 as a single term and finding the answer -16.

Question 4: Subtract 3x -4 from x^2+5x-7

When subtracting a 2 part expression, the negative sign needs to be applied to both parts of expression itself. This leads to the calculation step of x^2+5x-7-3x+4 and the correct answer in this case is x^2+2x-3. The misconception here is to only apply the negative to the 3x term, incorrectly resulting in the answer x^2+2x-11.

Prior knowledge is linked to misconceptions, as I have already discussed& it is my opinion from information I have read that a lack of prior knowledge greatly increases the probability and extent of misconceptions of mathematics. In the above examples, the misconceptions were that of bracket misuse and nothing else, but this misuse was a result of poor prior knowledge. Students presenting these errors are extremely unlikely to have been taught the methods incorrectly& it is the way in which they have remembered them in order to use them that causes such issue. By taking into account potential gaps in prior knowledge, and not assuming all children possess the same level of understanding of a previous topic, teachers can plan for pitfalls when a pupil says something along the lines of We ve never done this before or I don t know how to do that .

The act of differentiating an activity is all about making your lesson accessible to all students& under the inclusion guidelines. Through scaffolding questions using stretch activities and challenging the pupils, they are a lot more likely to enjoy, absorb and remember the lesson and content. By challenging the children with a choice, the onus is then on them and typically, schoolchildren will try to challenge themselves with something maybe a little too hard, but still something they can engage with. By doing so, the children can learn a new method or topic or even see some progress in their own eyes. Scaffolding questions and activities is a fine art& whilst the simpler questions must be easy enough for all students (including Lower Ability Students) but not so easy that they are a waste of time, much the same with the harder questions, they must still be doable by the students or there is no point in them being set. Simply put, you would not give year 8s work that ranges from year 2 content up to 2^nd year degree content& accessibility is key.

In order to track efficacy of lessons, or activities for precision, assessment for learning is the way forward. Even if it something quick and simply such as thumbs up, sideways or down, it gives the teacher some idea of who has understood it or who hasn t. I particularly dislike WWW and EBI in maths workbooks as no thought particularly goes into them as they are usually an end of the lesson action. Something I have observed a teacher doing is a list of 3 individual and pre-discussed SMART targets on the inside cover of each child s workbook and at the end of each lesson they assess honestly on a scale of 1-5 how well they think they worked towards achieving each target, it seems as though the students appreciate and enjoy this idea more as the teacher has sat down and agreed with them what they both think I a sensible outcome to expect and aspire towards& the pupils strive towards them moreso as they own their targets. I quickly adopted this into my pedagogy and hope to use it in my teaching career as a positive and mindful way to measure student progress.