Nancy Mack published a series of papers (Mack 1990, 1995, 2001) were she explores the possibility of using informal knowledge as a basis to teach fraction operations with reasoning (as opposed to emphasizing procedures).
Firstly, she focused on addition and subtraction (Mack 1990, 1995) and then on multiplication (Mack, 2001).
In the later, after collecting data from individual instructional session with average ability students, she concluded that it is possible to rely on the informal knowledge of "partitioning into equal parts" to promote reasoning about questions related to multiplication of fractions. Her analysis showed that, with proper instruction, the students were able to apply their informal knowledge in a host of different questions formulated in therms of "real life problems".
However, when it comes to addition and subtraction, the author concluded that the informal knowledge suffered the interference of rote procedures and integer number bias and the students were not able to capitalize on it to solve the questions as they were with multiplication of fractions. She stresses that the students were able to solve questions formulated in terms of "real life problems" not not when formulated symbolically. This phenomena was observed even after direct instruction.
In my research, I am focusing only on addition and subtraction of fraction and, so far, it seems that the extensive use of visual representations (rectangular area model for fractions) are enabling the use not only to solve symbolic and contextualized questions, but also explain verbally how and why they solved the questions the way they did.
What I expect by the end of my research project is to collect evidences that the visual representations are effective as basis for students to reason about addition and subtraction of fractions and a in depth description of the sequence of lessons used to achieve that goal.
Mack, N. K. (1990). Learning Fractions with Understanding: Building on Informal Knowledge. Journal for Research in Mathematics Education, 21(1).
Mack, N. K. (1995). Confounding whole-number and fraction concepts when building an informal knowledge. Journal for Research in Mathematics Education, 26(5).
Mack, N. K. (2001). Building on Informal Knowledge through Instruction in a Complex Content Domain: Partitioning, Units, and Understanding Multiplication of Fractions. Journal for Research in Mathematics Education, 32(3).
Nottingham is full of breweries. So far, I know the following: Castle Rock, Blue Monkey, Nottingham Brewery and Navigation. If you know any other, please, send me an email telling the name and where to find a good pint of it :)
I intend to include in this list pubs in Nottingham that sells good beer not from Nottingham, such as the Junk Yard. Soon.
1) Blue Monkey
I had a really good first impression, but the last Blue Monkeys I tried were not particularly good. I plan to drink more soon and then form an opinion. Not easy to find in pubs (except by the Organ Grinder, official tap of the brewery) but available bottled.
Their stout "Twisted Genius", is common in pubs around the city and it is my standard option in pubs with nothing new to try. I recommend: not brilliant, but good and for a reasonable price.
2) Castle Rock
It can be found bottled and in some pubs in Nottingham. In my opinion, it is the easier local beer, maybe too easy, but still a good choice.
4) Nottingham Brewery
My favourite! That is why I included the map right here.
The book 1001 beers to drink before die recommends their Extra Pale Ale and so do I. Good balance in the flavour. However, my favourite is the Oatmeal Stout, only produced during winter. It is fantastic! The best stout I have ever drunk (and I really like stouts!).
The official tap is a very local and traditional pub, with kind customers and staff. According to my experience, I would say this is a very typical British pub. They do not serve food, except on Quiz nights (Thursday) when the food is free!
First of all, I have to say that I am very Italian when it comes to coffee. I like short espressos and dark roasted beans.
After two years living in Nottingham, here are my favourites:
Located in a hidden alley in the city centre, this place is charming inside and offers a big variety of coffees from around the world. I tasted a few of them and my favourite is from Papua New Guinea. My girlfriend prefers the Peru feminino.
I also recommend the muffin. It is not homemade, but it is pretty good.
2) Ugly bread
Coffee is not their speciality, but they do it pretty well! The place is full of delicious bread, therefore, I would recommend them if you intend to drink coffee after lunch.
Unfortunately, they recently change to a more light roasted coffee, which is a deal breaker for me.
3) 200 degrees
I like the fact they tell the clients the roast of each blend available. In general, they lean towards lighter roasts, but they have some darker options.
Also, there are some places that I expected to drink a better coffee and got disappointed. Here they are:
1) All classic chains
Costa, Nero and Starbucks. The last is the better between them, but not good enough to worth a visit.
2) Jamie Oliver's Italian restaurant
The coffee is just average, what is not acceptable for a place "proud of being Italian".
Some facebook lists included Wired as one of the best coffees in Nottingham. I gave it a try and do not recommend! Very light roast, very acid coffee.
There are some interesting options for those who like light roasted coffee (more fruity and acid). My suggestions are Outpost (in the Lace Market) and The Specialty Coffee Shop (at Friar Lane).