Disclosure: I'm a mathematical biologist that came into it from the biology side.

I don't think it is necessary to retrain the biologists so they understand maths and retrain the mathematicians so they understand biologists, although these things should occur naturally to some degree with interdisciplinary work. Rather, I think it is important to understand the motivations of each 'type' and to tailor the language to the audience.

If you are coming from a quantitative background, I think it is important to realise how minimal many biologists' mathematical/computational skills are. This applies to undergrads to PhD students to postdocs to full professors collaborating with applied mathematicians, although obviously there are exceptions. I've taught in senior-level biology undergrad courses where some students are unable to rearrange simple algebraic statements. I know of biology professors that could quite rightly state they do good work in computational biology who could not program a single line or understand any of the maths. OTOH, I've seen applied mathematicians who have analysed data sets and have no idea what to make of the data. At this point, I often hear 'we ask the experimentalists what it means' or something along those lines.

To grossly generalise, biologists are more interested in quantitative methods as a tool to answer an interesting biological question and mathematicians are more interested in the method/analysis used to answer that question.

So when mathematicians talk to biologists, they need to place less emphasis on the technical details of a model/analysis and focus on the general features. For example, if you are building a model to answer an evolutionary or ecological question, a biologist is more interested in the biological assumptions the model is making and whether or not the model is a reasonable abstraction of the biological system. In turn, the mathematician may need to explain why certain details of the system can't or shouldn't be included in the model (e.g. because they would complicate the analysis for little gain in intuitive understanding).

When biologists talk to mathematicians they need to frame their questions in a way that is conducive to a quantitative framework. If a mathematician is trying to build a model, they don't need or want to know every minute detail of a system. It's overkill and will just lead to confusion. What are the most relevant points? For example, if a biologist is interested in how the density of cows affects the density of grass in a paddock, then it isn't helpful for the biologist to give the mathematician a lesson on all the intricacies of grass growing and grass eating. It would be better if the biologist comes with a defined question, such as 'how does increasing the number of cows in a paddock affect grass regeneration?' and pointing out that the main elements in the system are 1. how grass grows (as some function of grass density) and 2. how grass is eaten (as some function of cow density).

If you want a book about mathematical biology that is written for biologists then I'd recommend "A Biologist's Guide to Mathematical Modeling in Ecology and Evolution" by Sarah P. Otto & Troy Day

Disclosure: I'm a mathematical biologist that came into it from the biology side.

I don't think it is necessary to retrain the biologists so they understand maths and retrain the mathematicians so they understand biologists, although these things should occur naturally to some degree with interdisciplinary work. Rather, I think it is important to understand the motivations of each 'type' and to tailor the language to the audience.

To grossly generalise, biologists are more interested in quantitative methods as a tool to answer interesting biological questions and mathematicians are more interested in the method/analysis used to answer that question.

So when mathematicians talk to biologists, they need to place less emphasis on the technical details of a model/analysis and focus on the general features. For example, if you are building a model to answer an evolutionary or ecological question, a biologist is more interested in the biological assumptions the model is making and whether or not the model is a reasonable abstraction of the biological system. In turn, the mathematician may need to explain why certain details of the system can't or shouldn't be included in the model (e.g. because they would complicate the analysis for little gain in intuitive understanding).

When biologists talk to mathematicians they need to frame their questions in a way that is conducive to a quantitative framework. If a mathematician is trying to build a model, they don't need or want to know every minute detail of a system. It's overkill and will just lead to confusion. What are the most relevant points? For example, if a biologist is interested in how the density of cows affects the density of grass in a paddock, then it isn't helpful for the biologist to give the mathematician a lesson on all the intricacies of grass growing and grass eating. It would be better if the biologist comes with a defined question, such as 'how does increasing the number of cows in a paddock affect grass regeneration?' and points out that the main elements in the system are 1. how grass grows (as some function of grass density) and 2. how grass is eaten (as some function of cow density).

If you want a book about mathematical biology that is written for biologists then I'd recommend "A Biologist's Guide to Mathematical Modeling in Ecology and Evolution" by Sarah P. Otto & Troy Day